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Gromoll–Meyer's actions and the geometry of (exotic) spacetimes Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-03-13 Leonardo F. Cavenaghi, Lino Grama
Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a different smooth structure assumption to some classical known model could produce different physical meanings. Motivated by the works , , in this paper, we inaugurate
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Structures of sympathetic Lie conformal superalgebras Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-03-12 Meher Abdaoui
In this paper, we'll introduce the concept of sympathetic Lie conformal superalgebras and show that some classical properties of Lie conformal superalgebras are still valid for sympathetic Lie conformal superalgebras. We prove that the unique decomposition of each sympathetic Lie conformal superalgebra into a direct sum of indecomposable sympathetic ideals. We also show the existence of a greatest
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Convergence rate of the weighted Yamabe flow Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-02-28 Pak Tung Ho, Jinwoo Shin, Zetian Yan
The weighted Yamabe flow is the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the weighted Yamabe flow.
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On weakly stretch Kropina metrics Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-02-21 A. Tayebi, F. Barati
In this paper, we study weakly stretch Kropina metrics and prove a rigidity theorem. We show that the associated one-form of a weakly stretch Kropina metric is conformally Killing with respect to the associated Riemannian metric. We find that any weakly stretch Kropina metric has vanishing S-curvature. Then, we prove that every weakly stretch Kropina metric is a Berwald metric. It turns out that every
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Landsberg Finsler warped product metrics with zero flag curvature Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-02-21 D, a, x, i, a, o, , Z, h, e, n, g
In this paper, we study Finsler warped product metrics. We obtain the differential equations that characterize Landsberg Finsler warped product metrics. By solving these equations, we obtain the expression of these metrics. Furthermore, we construct a class of almost regular Finsler warped product metrics with the following properties: (1) is a Landsberg metric; (2) is not a Berwald metric; (3) has
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The category of [formula omitted]graded manifolds: What happens if you do not stay positive Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-02-01 Alexei Kotov, Vladimir Salnikov
In this paper we discuss the categorical properties of -graded manifolds. We start by describing the local model paying special attention to the differences in comparison to the -graded case. In particular we explain the origin of formality for the functional space and spell-out the structure of the power series. Then we make this construction intrinsic using a new type of filtrations. This sums up
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On homogeneous closed gradient Laplacian solitons Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-31 N, i, c, h, o, l, a, s, , N, g
We prove a structure theorem for homogeneous closed gradient Laplacian solitons and use it to show some examples of closed Laplacian solitons cannot be made gradient. More specifically, we show that the Laplacian solitons on nilpotent Lie groups found by Nicolini are not gradient up to homothetic -structures except for , where the potential function must be of a certain form. We also show that one
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The S-curvature of Finsler warped product metrics Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-26 Mehran Gabrani, Bahman Rezaei, Esra Sengelen Sevim
The class of warped product metrics can often be interpreted as key space models for general theory of relativity and in the theory of space-time structure. In this paper, we study one of the most important non-Riemannian quantities in Finsler geometry which is called the S-curvature. We examined the behavior of the S-curvature in the Finsler warped product metrics. We are going to prove that every
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Remarks on exact G2-structures on compact manifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-25 A, a, r, o, n, , K, e, n, n, o, n
An important open question related to the study of -holonomy manifolds concerns whether or not a compact seven-manifold can support an exact -structure. To provide insight into this question, we identify various relationships between the two-form underlying an exact -structure, the torsion of the -structure, and the curvatures of the associated metric. In addition to establishing identities valid for
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Prolongations, invariants, and fundamental identities of geometric structures Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-16 Jaehyun Hong, Tohru Morimoto
Working in the framework of nilpotent geometry, we give a unified scheme for the equivalence problem of geometric structures which extends and integrates the earlier works by Cartan, Singer-Sternberg, Tanaka, and Morimoto.
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Traveling along horizontal broken geodesics of a homogeneous Finsler submersion Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-15 Marcos M. Alexandrino, Fernando M. Escobosa, Marcelo K. Inagaki
In this paper, we discuss how to travel along horizontal broken geodesics of a homogeneous Finsler submersion, i.e., we study, what in Riemannian geometry was called by Wilking, the dual leaves. More precisely, we investigate the attainable sets of the set of analytic vector fields determined by the family of horizontal unit geodesic vector fields to the fibers of a homogeneous analytic Finsler submersion
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A normal line congruence and minimal ruled Lagrangian submanifolds in [formula omitted] Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-09 Jong Taek Cho, Makoto Kimura
We characterize Lagrangian submanifolds in complex projective space for which each parallel submanifold along normal geodesics with respect to a unit normal vector field is Lagrangian, by using a normal line congruence of the Lagrangian submanifold to complex 2-plane Grassmannian and quaternionic Kähler structure. As a special case, we can construct minimal ruled Lagrangian submanifolds in complex
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Antipodal sets of pseudo-Riemannian symmetric R-spaces Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-08 K, y, o, j, i, , S, u, g, i, m, o, t, o
We show that antipodal sets of pseudo-Riemannian symmetric -spaces associated with non-degenerate Jordan triple systems satisfy the following two properties: (1) Any antipodal set is included in a great antipodal set, and (2) any two great antipodal sets are transformed into each other by an isometry.
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On the prescribed fractional Q-curvatures problem on [formula omitted] under pinching conditions Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-03 Zhongwei Tang, Ning Zhou
In this paper, we study the prescribed fractional -curvatures problem of order 2 on the -dimensional standard sphere , where , . By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.
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When are shrinking gradient Ricci soliton compact Differ. Geom. Appl. (IF 0.5) Pub Date : 2024-01-02 Yuanyuan Qu, Guoqiang Wu
Suppose is a complete shrinking gradient Ricci soliton. We give a sufficient condition for a soliton to be compact, generalizing previous result of Munteanu-Wang . As an application, we give a classification of under some natural conditions.
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Morse-Novikov cohomology on foliated manifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-22 M, d, ., , S, h, a, r, i, f, u, l, , I, s, l, a, m
The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential , where is a closed 1-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance and then extend it to more general type of
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The energy density of biharmonic quadratic maps between spheres Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-21 Rareş Ambrosie, Cezar Oniciuc
In this paper, we first prove that a quadratic form from to is non-harmonic biharmonic if and only if it has constant energy density . Then, we give a positive answer to an open problem raised in concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic
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Bifurcations of robust features on surfaces in the Minkowski 3-space Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-21 M, a, r, c, o, , A, n, t, ô, n, i, o, , d, o, , C, o, u, t, o, , F, e, r, n, a, n, d, e, s
We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the lines principal curvature, the parabolic curve and the locus of points where the mean curvature vanishes.
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Vortex-type equations on compact Riemann surfaces Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-19 K, a, r, t, i, c, k, , G, h, o, s, h
In this paper, we prove estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle Monge-Ampère equation, prove an existence and uniqueness theorem for the Calabi-Yang-Mills equations on vortex bundles and get estimates for -vortex equation. We prove an existence and uniqueness result relating Gieseker stability and the
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Existence and uniqueness results for a singular Kirchhoff type equation on a closed manifold Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-15 Mohamed El Farouk Ounane, Kamel Tahri
Using the variational methods and the critical points theory, we prove the existence and the uniqueness of a positive solution for a singular Kirchhoff type equation on a closed Riemannian manifold of dimension . At the end, we give a geometric application involving the conformal Laplacian.
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Sphere bundle over the set of inner products in a Hilbert space Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-14 E. Andruchow, M.E. Di Iorio y Lucero
Let be a complex Hilbert space and the space of bounded linear operators in . Any other equivalent inner product in is of the form () for some positive invertible operator . In this paper we study the bundle which consist of the unit sphere over each (equivalent) inner product , which due to the observation above can be defined We prove that is a complemented submanifold of the Banach space and a homogeneous
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First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-13 Pak Tung Ho, Juncheol Pyo
In this note, we consider the first nonzero eigenvalue of the -Laplacian on free boundary proper hypersurfaces in the unit ball evolving along the inverse mean curvature flow. We show that is monotone decreasing along the flow. Using the convergence of free boundary disks in the unit ball, we give a lower bound of of a free boundary disk type hypersurface in the unit ball.
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Chekanov torus and Gelfand–Zeitlin torus in S2 × S2 Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-12-07 Y, o, o, s, i, k, , K, i, m
The Chekanov torus is the first known torus, a monotone Lagrangian torus that is not Hamiltonian isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in and a monotone Lagrangian torus that had been constructed before Chekanov's construction . We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the
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On the geometry of conullity two manifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-23 Jacob Van Hook
We consider complete locally irreducible conullity two Riemannian manifolds with constant scalar curvature along nullity geodesics. There exists a naturally defined open dense subset on which we describe the metric in terms of several functions which are uniquely determined up to isometry. In addition, we show that the fundamental group is either trivial or infinite cyclic.
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S-curvature, E-curvature, and Berwald scalar curvature of Finsler spaces Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-21 M. Crampin
I show that the S-curvature of a Finsler space vanishes if and only if the E-curvature vanishes if and only if the Berwald scalar curvature vanishes; and I extend these results to the case in which these objects are isotropic.
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Quasi-Einstein manifolds admitting a closed conformal vector field Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-24 J.F. Silva Filho
In this article, we investigate quasi-Einstein manifolds admitting a closed conformal vector field. Initially, we present a rigidity result for quasi-Einstein manifolds with constant scalar curvature and carrying a non-parallel closed conformal vector field. Moreover, we prove that quasi-Einstein manifolds admitting a closed conformal vector field can be conformally changed to constant scalar curvature
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The Brylinski beta function of a double layer Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-21 Pooja Rani, M.K. Vemuri
An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution T on d-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If T is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants
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Vector bundles on real abelian varieties Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-19 Archana S. Morye
This paper is about real holomorphic vector bundles on real abelian varieties. The main result of the paper gives several conditions that are necessary and sufficient for the existence of a holomorphic connection on a real holomorphic vector bundle over a real abelian variety. Also proved is an analogue, for real abelian varieties, of a result of Simpson, which gives a criterion for a holomorphic vector
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Torsion-free connections on G-structures Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-19 Brice Flamencourt
We prove that for a Lie group SOn(R)⊂G⊂GLn(R), any G-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.
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Legendre magnetic flows for totally η-umbilic real hypersurfaces in a complex hyperbolic space Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-19 Qingsong Shi, Toshiaki Adachi
We study trajectories for Sasakian magnetic fields on horospheres, on geodesic spheres and on tubes around totally geodesic complex hypersurfaces in a complex hyperbolic space. Considering the subbundle formed by unit tangent vectors orthogonal to the characteristic vector field, flows associated with trajectories on this subbundle are smoothly conjugate to each other for each geodesic sphere, and
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Holomorphic projective connections on surfaces Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-16 Oumar Wone
We study complex analytic projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the first and second derivatives, and with holomorphic coefficients.
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The maximal curves and heat flow in general-affine geometry Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-15 Yun Yang
In Euclidean geometry, the shortest distance between two points is a straight line. Chern made a conjecture (cf. [11]) in 1977 that an affine maximal graph of a smooth and locally uniformly convex function on two-dimensional Euclidean space R2 must be a paraboloid. In 2000, Trudinger and Wang completed the proof of this conjecture in affine geometry (cf. [47]). (Caution: in these literatures, the term
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The lifts of surfaces in neutral 4-manifolds into the 2-Grassmann bundles Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-13 Naoya Ando
A twistor lift of a space-like or time-like surface in a neutral hyperKähler 4-manifold with zero mean curvature vector is given by a (para)holomorphic function, which yields (para)holomorphicity of the Gauss maps of space-like or time-like surfaces in E24 with zero mean curvature vector. For a space-like or time-like surface in an oriented neutral 4-manifold with zero mean curvature vector such that
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Moment maps and isoparametric hypersurfaces in spheres — Grassmannian cases Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-11-07 Shinobu Fujii
We expect that every Cartan–Münzner polynomial of degree four can be described as a squared-norm of a moment map for a Hamiltonian action. Our expectation is known to be true for Hermitian cases, that is, those obtained from the isotropy representations of compact irreducible Hermitian symmetric spaces of rank two. In this paper, we prove that our expectation is true for the Cartan–Münzner polynomials
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Rarita-Schwinger fields on nearly Kähler manifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-25 Soma Ohno, Takuma Tomihisa
We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of Rarita-Schwinger fields coincides with the space of harmonic 3-forms. Applying the same technique to deformation theory
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Lower bounds for isoperimetric profiles and Yamabe constants Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-17 Juan Miguel Ruiz, Areli Vázquez Juárez
We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, (Mm×Rn,g+gE), m,n>1. In particular, we introduce a lower bound for the isoperimetric profile of Mm×Rn for regions of large volume and we improve on previous estimates of lower bounds for the isoperimetric profiles of S2×R2, S3×R2, S2×R3. We also
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Periodic discrete Darboux transforms Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-18 Joseph Cho, Katrin Leschke, Yuta Ogata
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations
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Geometric integral formulas of cylinders within slabs Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-17 Ximo Gual-Arnau
We present new expressions for the integrals of mean curvature of domains in Rn by means of sections with cylinders. Then, we combine these expressions with the corresponding version of the invariant density of affine subspaces in Rn, in order to obtain pseudo-rotational formulae for all the integrals of mean curvature of ∂K. As particular cases, we present pseudo-rotational integral formulas for the
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Classification of semi-parallel hypersurfaces of the product of two spheres Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-13 Shujie Zhai, Cheng Xing
It is known that Mendonça and Tojeiro (2013) [19] have established a complete classification of parallel submanifolds in the product manifold Qk1n1×Qk2n2, where Qk1n1 (resp. Qk2n2) is an n1-dimensional (resp. n2-dimensional) real space form with constant curvature k1 (resp. k2). In this paper, motivated by this result with considering further generalization, we study those semi-parallel hypersurfaces
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Gronwall's conjecture for 3-webs with two pencils of lines Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-13 Sergey I. Agafonov
We prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion.
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Pseudo-Conformal actions of the Möbius group Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-11 M. Belraouti, M. Deffaf, Y. Raffed, A. Zeghib
We study compact connected pseudo-Riemannian manifolds (M,g) on which the conformal group Conf(M,g) acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of Conf(M,g) is the Möbius group, then (M,g) is conformally flat.
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Geometry and topology of manifolds with integral radial curvature bounds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-10-06 Jing Mao
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
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Some geometric properties of normal and tangent submanifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-09-27 Josué Meléndez, Eduardo Rodríguez-Romero
In this paper we study some special ruled surfaces in a 3-dimensional Riemannian manifold M¯. Given an immersed surface M into M¯, we consider the ruled surfaces that are normal or tangent to M and give some geometric relations between them, generalizing some recent results obtained in [3], [5]. We also give some general properties on normal and tangent submanifolds of arbitrary dimension.
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Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-09-28 Zejun Hu, Xi Zhang
Wang and Zhang in (2022) [20] and (2023) [21] characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator Lξ or contact Lie operator Lξϕ. In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized
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On isoperimetric problem in 2-dimensional Randers space Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-09-28 Hongmei Zhu, Ranran Li
In this paper, we prove that the circle centered at the origin in B2(δξ) is a proper maximum of the isoperimetric problem in a 2-dimensional Randers space endowed with 3-parameter family of non-locally projectively flat Finsler metrics of non-constant isotropic S-curvature.
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Harmonic G2-structures on almost Abelian Lie groups Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-09-19 Andrés J. Moreno
We consider left-invariant G2-structures on 7-dimensional almost Abelian Lie groups. Also, we characterise the associated torsion forms and the full torsion tensor according to the Lie bracket A of the corresponding Lie algebra. In those terms, we establish the algebraic condition on A for each of the possible 16-torsion classes of a G2-structure. In particular, we show that four of those torsion classes
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On recurrent Riemannian and Ricci curvatures of Finsler metrics Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-08-23 H. Faraji, A. Tayebi, B. Najafi
In this paper, we study a property of Riemannian and Ricci curvatures under which it reproduces itself, namely, recurrent Finsler metrics. We prove that if (M,F) is a recurrent Finsler manifold of non-zero isotropic flag curvature, then F is a Landsberg metric. It follows that Every positively complete 2-dimensional Randers metric is recurrent if and only if it is a Riemannian or locally Minkowskian
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Homogeneous nonlinear splittings and Finsler submersions Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-08-17 S. Hajdú, T. Mestdag
A nonlinear splitting on a fiber bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the total manifold of a fiber bundle. We show how homogeneous nonlinear splittings and nonlinear lifts can be used to construct submersions between Euclidean, Minkowski and Finsler spaces. As an application we consider a semisimple
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Gelfand duality for manifolds, and vector and other bundles Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-08-16 Andrew D. Lewis
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a smooth manifold in the topological dual of its algebra of smooth functions. This is generalised here in two directions. First, the topological embeddings
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On P-reducibility of general (α,β)-metrics Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-08-14 Liulin Liu, Xiaoling Zhang
The class of P-reducible manifolds was first introduced by Matsumoto. This class of Finsler manifolds contains the classes of C-reducible manifolds, Berwald manifolds and Landsberg manifolds. In 1977, Matsumoto and Shimada proposed an open problem: Is there any concrete P-reducible metric which is not C-reducible? For this aim, we study a class of Finsler metrics called general (α,β)-metrics. We find
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Time analyticity for the parabolic type Schrödinger equation on Riemannian manifold with integral Ricci curvature condition Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-08-01 Wen Wang
In the paper, we investigate the pointwise time analyticity of the parabolic type Schrödinger equation on a complete Riemannian manifold with integral Ricci curvature condition.
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Existence of a variational principle for PDEs with symmetries and current conservation Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-26 Markus Dafinger
It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a differential equation, which satisfies sufficiently many symmetries and corresponding conservation laws, leads to a variational functional, whose Euler-Lagrange equation is the given differential equation
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Geometry of cascade feedback linearizable control systems Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-26 Taylor J. Klotz
Cascade feedback linearization provides geometric insights on explicit integrability of nonlinear control systems with symmetry. A central piece of the theory requires that the partial contact curve reduction of the contact sub-connection be static feedback linearizable. This work establishes new necessary conditions on the equations of Lie type - in the abelian case - that arise in a contact sub-connection
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Riemannian exponential and quantization Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-25 J. Muñoz-Díaz, R.J. Alonso-Blanco
This article continues and completes the previous one [18]. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the one presented in [18]. The two methods allow quantization of functions that come from covariant tensor fields. The equivalence of both is demonstrated as a consequence of a remarkable property of
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Some characterizations of Bach solitons via Ricci curvature Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-25 Antonio W. Cunha, Eudes L. de Lima, Rong Mi
In this short note we provide some results for Bach solitons under different assumptions. In fact, under either non-negative or non-positive Ricci curvature condition we are able to show that a Bach soliton must be Bach-flat, since it satisfies a finite weighted Dirichlet integral condition or a parabolicity condition jointly with some regularity conditions L∞ or Lp on gradient of the potential function
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Diameter estimates for submanifolds in manifolds with nonnegative curvature Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-20
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we
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On the rigidity of the Sasakian structure and characterization of cosymplectic manifolds Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-18
We introduce new metric structures on a smooth manifold (called “weak” structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures (φ,ξ,η,g) and allow us to take a fresh look at the classical theory and find new applications. This assertion is illustrated by generalizing several well-known results. It is proved that any Sasakian structure is rigid, i.e., our weak
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Existence of Lie algebroids on the tangent bundle with a given anchor map of constant rank Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-07-12
We show that given a constant rank linear map, K:TM→TM, there exists a Lie algebroid with K as its anchor map, if and only if the image distribution, ImK, is involutive. As a byproduct, a new example of Lie algebroid bracket associated with a regular foliation is obtained through the projector onto the involutive distribution. The Lie algebroid bracket is not defined on the involutive distribution
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Equidistant sets on Alexandrov surfaces Differ. Geom. Appl. (IF 0.5) Pub Date : 2023-06-28 Logan S. Fox, J.J.P. Veerman
We examine properties of equidistant sets determined by nonempty disjoint compact subsets of a compact 2-dimensional Alexandrov space (of curvature bounded below). The work here generalizes many of the known results for equidistant sets determined by two distinct points on a compact Riemannian 2-manifold. Notably, we find that the equidistant set is always a finite simplicial 1-complex. These results