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  • Equivariance and algebraic relations for curves
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-29
    Chris Athorne

    We generalise a classical argument for deducing algebraic models of Riemann surfaces from the Riemann–Roch theorem. The method involves counting arguments based on equivariant resolutions.

    更新日期:2020-05-29
  • On equivalence of the second order linear differential operators, acting in vector bundles
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-29
    Valentin Lychagin

    The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally associated with differential operators, are found. These geometrical structures are used to solve the problems of local as well as global equivalence of differential operators.

    更新日期:2020-05-29
  • On δ-Hom-Jordan Lie conformal superalgebras
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-29
    Shuangjian Guo; Shengxiang Wang

    In this paper, we introduce the representation theory of δ-Hom-Jordan Lie conformal superalgebras and discuss the case of adjoint representations. Furthermore, we develop the cohomology theory of δ-Hom-Jordan Lie conformal superalgebras and discuss some applications to the study of deformations of regular δ-Hom-Jordan Lie conformal superalgebras. Finally, we introduce derivations of multiplicative

    更新日期:2020-05-29
  • Poisson brackets in Kontsevich’s “Lie World”
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-29
    Florian Naef

    In this note we develop the theory of double brackets in the sense of van den Bergh (2008) in Kontsevich’s non-commutative “Lie World”. These double brackets can be thought of as Poisson structures defined by formal expressions only involving the structure maps of a quadratic Lie algebra. The basic example is the Kirillov-Kostant-Souriau (KKS) Poisson bracket. We introduce a notion of non-degenerate

    更新日期:2020-05-29
  • On semi-quasi-Einstein manifold
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-27
    Yanling Han; Avik De; Peibiao Zhao

    In the present paper we introduce a semi-quasi-Einstein manifold from a semi symmetric metric connection. Among others, the popular Schwarzschild and Kottler spacetimes are shown to possess this structure. Certain curvature conditions are studied in such a manifold with a Killing generator.

    更新日期:2020-05-27
  • Quasi-Poisson structures on moduli spaces of quasi-surfaces
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-27
    Vladimir Turaev

    In generalization of the classical Atiyah–Bott Poisson brackets on the moduli spaces of surfaces we define quasi-Poisson brackets on the moduli spaces of quasi-surfaces.

    更新日期:2020-05-27
  • Rational limit cycles on Bernoulli and Riccati equations
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-21
    Clàudia Valls

    In this paper we deal with Bernoulli equations dy∕dx=A(x)yn+B(x)y, where A(x) and B(x) are real polynomials with A(x)⁄≡0 and n≥3. We prove that these Bernoulli equations can have at most 2 rational limit cycles if n is odd and at most one rational limit cycle if n is even. We also provide examples of Bernoulli equations with these numbers of rational limit cycles. Moreover we deal with the Riccati

    更新日期:2020-05-21
  • Shortest and straightest geodesics in sub-Riemannian geometry
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-19
    Dmitri Alekseevsky

    There are several different, but equivalent definitions of geodesics in a Riemannian manifold, based on two characteristic properties: geodesics as shortest curves and geodesics as straightest curves. They are generalized to sub-Riemannian manifolds, but become non-equivalent. We give an overview of different approaches to the definition, study and generalization of sub-Riemannian geodesics and discuss

    更新日期:2020-05-19
  • Ricci-like solitons on almost contact B-metric manifolds
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-19
    Mancho Manev

    Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the

    更新日期:2020-05-19
  • Gradient estimates for a weighted nonlinear elliptic equation and Liouville type theorems
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-19
    Abimbola Abolarinwa

    This paper proves local gradient estimates on positive solutions to the following nonlinear elliptic equation Δfu+au(logu)α=0,where a and α are real constants, on complete weighted manifolds with Bakry–Émery Ricci tensor bounded from below. For applications, global estimates and some Liouville type theorems are derived.

    更新日期:2020-05-19
  • Separation of variables, Lax-integrable systems and gl(2)⊗gl(2)-valued classical r-matrices
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-15
    T. Skrypnyk

    In the present paper we consider a problem of separation of variables for Lax-integrable hamiltonian system generated by general non-skew-symmetric gl(2)⊗gl(2)-valued classical r-matrix r(u,v) with spectral parameters. We specify the general separability condition of Dubrovin and Skrypnyk (2018) on the components of the r-matrix and consider two new classes of examples of classical non-skew-symmetric

    更新日期:2020-05-15
  • QCH Kähler surfaces II
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-14
    Włodzimierz Jelonek

    In this paper we give new examples of QCH Kähler surfaces whose opposite almost Hermitian structure is Hermitian and not locally conformally Kähler. In this way we give also a large class of examples of Hermitian surfaces with J-invariant Ricci tensor which are not l.c.k.

    更新日期:2020-05-14
  • Proper r-harmonic functions on the Thurston geometries
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-12
    Sigmundur Gudmundsson; Anna Siffert

    For any positive natural number r∈N+ we construct new explicit proper r-harmonic functions on the celebrated 3-dimensional Thurston geometries Sol, Nil, SL˜2(R), H2×R and S2×R.

    更新日期:2020-05-12
  • The Ricci curvature for noncommutative three tori
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-12
    Rui Dong; Asghar Ghorbanpour; Masoud Khalkhali

    We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the flat metric, the standard volume form on the noncommutative three torus is perturbed and the corresponding perturbed Laplacian is analysed. Using Connes’ pseudodifferential calculus for the noncommutative tori, we explicitly

    更新日期:2020-05-12
  • On integrability of transverse Lie–Poisson structures at nilpotent elements
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-11
    Yassir Dinar

    We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie–Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform construction of these integrable systems for an infinite family of distinguished

    更新日期:2020-05-11
  • Magnetic billiards: Non-integrability for strong magnetic field; Gutkin type examples
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-07
    Misha Bialy; Andrey E. Mironov; Lior Shalom

    We consider magnetic billiards under a strong constant magnetic field. The purpose of this paper is two-folded. We examine the question of existence of polynomial integral of billiard magnetic flow. As in our previous paper (Bialy and Mironov, 2016) we succeed to reduce this question to algebraic geometry test on existence of polynomial integral, which shows polynomial non-integrability for all but

    更新日期:2020-05-07
  • Kummer sandwiches and Greene–Plesser construction
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-06
    Noah Braeger; Andreas Malmendier; Yih Sung

    In the context of K3 mirror symmetry, the Greene–Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in P3, starting from a special one-parameter family of K3 varieties known as the quartic Dwork pencil. We show that certain K3 double covers obtained from the three-parameter family of quartic Kummer surfaces associated with a principally polarized abelian

    更新日期:2020-05-06
  • Equivariant Batalin–Vilkovisky formalism
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-05-05
    F. Bonechi; A.S. Cattaneo; J. Qiu; M. Zabzine

    We study an equivariant extension of the Batalin–Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang–Mills

    更新日期:2020-05-05
  • Symplectic groupoids for cluster manifolds
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-29
    Songhao Li; Dylan Rupel

    We construct symplectic groupoids integrating log-canonical Poisson structures on cluster varieties of type A and X over both the real and complex numbers. Extensions of these groupoids to the completions of the cluster varieties where cluster variables are allowed to vanish are also considered. In the real case, we construct source-simply-connected groupoids for the cluster charts via the Poisson

    更新日期:2020-04-29
  • An equivariant orbifold index for proper actions
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-28
    Peter Hochs; Hang Wang

    For a proper, cocompact action by a locally compact group of the form H×G, with H compact, we define an H×G-equivariant index of H-transversally elliptic operators, which takes values in KK∗(C∗H,C∗G). This simultaneously generalises the Baum–Connes analytic assembly map, Atiyah’s index of transversally elliptic operators, and Kawasaki’s orbifold index. This index also generalises the assembly map to

    更新日期:2020-04-28
  • Equivariant KK-theory for non-Hausdorff groupoids
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-28
    Lachlan E. MacDonald

    We give a detailed and unified survey of equivariant KK-theory over locally compact, second countable, locally Hausdorff groupoids. We indicate precisely how the “classical” proofs relating to the Kasparov product can be used almost word-for-word in this setting, and give proofs for several results which do not currently appear in the literature.

    更新日期:2020-04-28
  • Frame bundle approach to generalized minimal submanifolds
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-23
    Kamil Niedziałomski

    We extend the notion of r-minimality of a submanifold in arbitrary codimension to u-minimality for a multi-index u∈Nq, where q is the codimension. This approach is based on the analysis on the frame bundle of orthonormal frames of the normal bundle to a submanifold and vector bundles associated with this bundle. The notion of u-minimality comes from the variation of the σu–symmetric function obtained

    更新日期:2020-04-23
  • Symmetries, similarity invariant solution, conservation laws and exact solutions of the time-fractional Harmonic Oscillator equation
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-20
    Maryam Yourdkhany; Mehdi Nadjafikhah

    In this paper, group analysis of the time-fractional Harmonic Oscillator equation with Riemann–Liouville derivative is performed and its reduced fractional ordinary differential equations are determined. With the aid of the concept of nonlinear self-adjoint and the fractional generalization of the Noether operators are obtained conserved vector for this equation. Furthermore, by using Laplace transform

    更新日期:2020-04-20
  • Vertical genera
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-18
    Niccolò Salvatori; Simon Scott

    The classical construction of a genus on a closed manifold is extended to the case of families of manifolds parametrised by a space X. The genera considered here are built from certain generalised Pontryagin and Chern classes as maps from bordism cohomology to the singular cohomology of X.

    更新日期:2020-04-18
  • Mass functions of a compact manifold
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-18
    Andreas Hermann; Emmanuel Humbert

    Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a≥0↦X+M(a) (resp. a≥0↦X−M(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p∈M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green

    更新日期:2020-04-18
  • Harnack estimates for a nonlinear diffusion equation on compact Kähler manifolds
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-07
    Liangdi Zhang

    In this paper, we prove matrix and classical Harnack estimates for positive solutions to the nonlinear diffusion partial differential equation ∂tu=Δu+au+bup+1 on a compact Kähler manifold (with fixed metric). When the metric evolves under the normalized Kähler–Ricci flow, we also derive some matrix and classical Harnack estimates.

    更新日期:2020-04-07
  • Long-time asymptotics of a three-component coupled nonlinear Schrödinger system
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-07
    Wen-Xiu Ma

    Starting from a specific example of 4 × 4 matrix spectral problems, an integrable coupled hierarchy, which includes a three-component coupled nonlinear Schrödinger system as the first nonlinear one, is generated, and an associated oscillatory Riemann–Hilbert problem is formulated. With the nonlinear steepest descent method, the leading long-time asymptotics for the Cauchy problem of the three-component

    更新日期:2020-04-07
  • Superintegrable systems on 3 dimensional conformally flat spaces
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-04-07
    Allan P. Fordy; Qing Huang

    We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional quadratic first integrals, thus constructing a large class of superintegrable systems and the complete Poisson algebra of first integrals. We then use the isometries to reduce our systems to 2 degrees of freedom. For each

    更新日期:2020-04-07
  • Infinitesimal symmetries in contact Hamiltonian systems
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-03-27
    Manuel de León; Manuel Lainz Valcázar

    In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in contact dynamics, the existence of infinitesimal symmetries does not produce conserved quantities, but functions that dissipate at the same rate than the energy; so

    更新日期:2020-03-27
  • On some geometric properties of CR-submanifolds of a Sasakian manifold
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-03-24
    Süleyman Di̇ri̇k

    In this paper, we study the geometry of the contact CR-submanifolds of a Sasakian manifold. By searching the parallelism conditions of the tensors reduced in the submanifolds, some properties and results obtained from the definition of the contact CR-submanifolds are given. Also, necessary and sufficient conditions are given for a submanifold to be a contact CR-submanifold, contact CR-product, D, D⊥

    更新日期:2020-03-24
  • Central configurations in the planar 6-body problem forming two equilateral triangles
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-03-23
    Zhifu Xie; Gokul Bhusal; Hamas Tahir

    A Central Configuration (CC) is a special arrangement of masses in the n-body problem where the gravitational force on each body points proportionally toward the center of mass. A stacked CC is a CC that has a proper subset of the n bodies also forming a CC. In this paper, six bodies are located on two equilateral triangles Δ123 and Δ456. Assume that both triangles are symmetrical about the line connecting

    更新日期:2020-03-23
  • Beltrami vector fields with an icosahedral symmetry
    J. Geometr. Phys. (IF 0.806) Pub Date : 2020-03-21
    Giedrius Alkauskas

    A vector field is called a Beltrami vector field, if B×(∇×B)=0. In this paper we construct two unique Beltrami vector fields I and Y, such that ∇×I=I, ∇×Y=Y, and such that both have an orientation-preserving icosahedral symmetry. Both of them have an additional symmetry with respect to a non-trivial automorphism of the number field Q(5).

    更新日期:2020-03-21
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