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  • Almost-Kähler anti-self-dual metrics on K3#3CP2‾
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-21
    Inyoung Kim

    Donaldson-Friedman constructed anti-self-dual classes on K3#3CP2‾ using twistor space. We show that some of these conformal classes have almost-Kähler representatives.

    更新日期:2020-07-21
  • Biharmonic δ(r)-ideal hypersurfaces in Euclidean spaces are minimal
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-13
    Deepika; Andreas Arvanitoyeorgos

    A submanifold Mn of a Euclidean space EN is called biharmonic if ΔH→=0, where H→ is the mean curvature vector of Mn. A well known conjecture of B.Y. Chen states that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. Ideal submanifolds were introduced by Chen as those which receive the least possible tension at each point. In this paper we prove that every δ(r)-ideal biharmonic

    更新日期:2020-07-13
  • On mean curvature flow of singular Riemannian foliations: Noncompact cases
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-09
    Marcos M. Alexandrino; Leonardo F. Cavenaghi; Icaro Gonçalves

    In this paper we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Radeschi and the first author. We show that, under bounded curvature conditions, any finite time singularity is a singular leaf, and the singularity is of type I. The new techniques also allow us to discuss the existence of basins

    更新日期:2020-07-10
  • Poisson cohomology of broken Lefschetz fibrations
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-07
    Panagiotis Batakidis; Ramón Vera

    We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyanin algebra. As a side result, we give compact formulas for the Poisson coboundary

    更新日期:2020-07-07
  • About the eta–invariants of Berger spheres
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-03
    Gregor Weingart

    The integral of the top dimensional term of the multiplicative sequence of Pontryagin forms associated to an even formal power series is calculated for special Riemannian metrics on the unit ball of a hermitean vector space. Using this result we calculate the generating function of the reduced Dirac and signature η–invariants for the family of Berger metrics on the odd dimensional spheres.

    更新日期:2020-07-03
  • Harmonicity of vector fields on the oscillator groups with neutral signature
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-07-01
    Na Xu; Ju Tan

    In this paper, we mainly investigate curvature properties and harmonicity of invariant vector fields on the four-dimensional Oscillator groups endowed with three left-invariant pseudo-Riemannian metrics of signature (2,2). We determine all harmonic vector fields, vector fields which define harmonic maps and the vector fields which are critical points for the energy functional restricted to vector fields

    更新日期:2020-07-01
  • A note on invariant generators for generalized subbundles
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-25
    Qianqian Xia

    This note studies invariant generators for a certain class of invariant smooth generalized subbundles of exact Courant algebroids, which generalizes existing results for invariant vector subbundles of exact Courant algebroids. As a result, we provide a simple and geometric proof for Theorem 1 in [1].

    更新日期:2020-06-25
  • Projective structures on Riemann surface and natural differential operators
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-22
    Indranil Biswas; Sorin Dumitrescu

    We investigate the holomorphic differential operators on a Riemann surface M. This is done by endowing M with a projective structure. Let L be a theta characteristic on M. We explicitly describe the jet bundle Jk(E⊗L⊗n), where E is a holomorphic vector bundle over M equipped with a holomorphic connection, for all k and n. This provides a description of global holomorphic differential operators from

    更新日期:2020-06-22
  • Nodal solutions for a Paneitz-Branson type equation
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-17
    Seid Azaiz; Hichem Boughazi

    Let (M,g) be a smooth compact Riemannian manifold of dimension n≥5. Denote Lg the Paneitz-Branson type operator. In this paper, we show that there exists a nodal solution (solution with changing sign) of the nonlinear Paneitz-Branson type equation Lgv=ϵ|v|N−2v where ϵ<0. At the end, we give a geometric application of the above equation.

    更新日期:2020-06-17
  • Quasi-Einstein manifolds with structure of warped product
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-17
    Paula Correia; Romildo Pina

    In this paper we prove that, under certain conditions, in a quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all the quasi-Einstein manifolds when r-Bakry-Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n−1)-dimensional translation group and the fiber is Ricci-flat. As an

    更新日期:2020-06-17
  • On the first Betti number of spacetimes with parallel lightlike vector field
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-04
    Raymond Hounnonkpe

    We prove that a non-totally vicious n-dimensional compact spacetime (M,g) admitting a parallel lightlike vector field is foliated by compact totally geodesic null hypersurfaces. As a consequence, assuming non-negative Ricci curvature on the leaves then the first Betti number of M is bounded above by n with equality if and only if M is diffeomorphic to the torus.

    更新日期:2020-06-04
  • Surfaces with zero mean curvature vector in neutral 4-manifolds
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-06-04
    N. Ando

    Space-like surfaces and time-like surfaces with zero mean curvature vector in oriented neutral 4-manifolds are isotropic and compatible with the orientations of the spaces if and only if their lifts to the space-like and the time-like twistor spaces respectively are horizontal. In neutral Kähler surfaces and paraKähler surfaces, complex curves and paracomplex curves respectively are such surfaces and

    更新日期:2020-06-04
  • Harmonic manifolds of hypergeometric type and spherical Fourier transform
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-05-26
    Mitsuhiro Itoh; Hiroyasu Satoh

    The spherical Fourier transform on a harmonic Hadamard manifold (Xn,g) of positive volume entropy is studied. If (Xn,g) is of hypergeometric type, namely spherical functions of X are represented by the Gauss hypergeometric functions, the inversion formula, the convolution rule together with the Plancherel theorem are shown by the representation of the spherical functions in terms of the Gauss hypergeometric

    更新日期:2020-05-26
  • Lie groupoids and their natural transformations
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-05-14
    Olivier Brahic; Dion Pasievitch

    We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.

    更新日期:2020-05-14
  • On the volume of orbifold quotients of symmetric spaces
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-05-08
    Ilesanmi Adeboye; McKenzie Wang; Guofang Wei

    Key to H. C. Wang's quantitative study of Zassenhaus neighbourhoods of non-compact semisimple Lie groups are two constants that depend on the root system of the corresponding Lie algebra. This article extends the list of values for Wang's constants to the exceptional Lie groups and also removes their dependence on dimension. The first application is an improved upper sectional curvature bound for a

    更新日期:2020-05-08
  • On the cross curvature flow
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-27
    Pak Tung Ho; Jinwoo Shin

    In this paper, we study the cross curvature soliton. We study the cross curvature soliton with a warped product structure. On the other hand, we show that the volume entropy is decreasing along the cross curvature flow.

    更新日期:2020-04-27
  • Classification of gradient shrinking Ricci solitons with bounded Ricci curvature
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-27
    Fei Yang; Zijun Wang; Liangdi Zhang

    In this paper, we classify n-dimensional (n≥4) gradient shrinking Ricci solitons with bounded Ricci curvature. Precisely, we obtain that such a soliton satisfying Ric+Hessf=λg with 0≤Ric≤λng is a finite quotient of the Gaussian shrinking soliton Rn. In the case of dimension 4, we prove that a radially flat gradient shrinking Ricci soliton with 0≤Ric≤λ2g is a finite quotient of R4 or R2×S2.

    更新日期:2020-04-27
  • Extrinsic geometry of the Gromoll-Meyer sphere
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-27
    Chao Qian; Zizhou Tang; Wenjiao Yan

    Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotient N˜11=(Sp(2)×S4)/S3, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Furthermore, on the quotient N˜11/S3, we construct a transnormal system with transnormal hypersurfaces diffeomorphic

    更新日期:2020-04-27
  • Canonical Lorentzian spin structure and twistor spinors on the Fefferman space of a contact Riemannian manifold
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-24
    Masayoshi Nagase; Toki Ohyama

    The Fefferman space of a contact Riemannian manifold carries a Lorentzian spin structure canonically. On the Lorentzian spin manifold, we investigate the Dirac operator and the twistor operator closely. In particular, we show that, if the contact Riemannian manifold is integrable, then there exist non-zero global solutions of the twistor equation.

    更新日期:2020-04-24
  • A family of MCF solutions for the Heisenberg group
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-23
    Adriana Araujo Cintra; Benedito Leandro; Hiuri Fellipe dos Santos Reis

    The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group H when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by Iso0(H) (the isometries of H for which the origin is a fix point). We conclude that the function which describe the motion of these surfaces under MCF, is always a linear affine

    更新日期:2020-04-23
  • Basic structures on derived critical loci
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2020-04-23
    Gabriele Vezzosi

    We review the derived algebraic geometry of derived zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we some of the structures carried by derived critical loci: the homotopy Batalin-Vilkovisky structure, the action of the 2-monoid of the self-intersection of the zero section, and the derived symplectic structure of degree −1. We also show how

    更新日期:2020-04-23
  • Anomaly formulas for the complex-valued analytic torsion on compact bordisms.
    Differ. Geom. Appl. (IF 0.556) Pub Date : 2013-06-01
    Osmar Maldonado Molina

    We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued

    更新日期:2019-11-01
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