Harmonic manifolds of hypergeometric type and spherical Fourier transform Differ. Geom. Appl. (IF 0.605) 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
Lie groupoids and their natural transformations Differ. Geom. Appl. (IF 0.605) 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.
On the volume of orbifold quotients of symmetric spaces Differ. Geom. Appl. (IF 0.605) 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
On the cross curvature flow Differ. Geom. Appl. (IF 0.605) 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.
Classification of gradient shrinking Ricci solitons with bounded Ricci curvature Differ. Geom. Appl. (IF 0.605) 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.
Extrinsic geometry of the Gromoll-Meyer sphere Differ. Geom. Appl. (IF 0.605) 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
Canonical Lorentzian spin structure and twistor spinors on the Fefferman space of a contact Riemannian manifold Differ. Geom. Appl. (IF 0.605) 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.
A family of MCF solutions for the Heisenberg group Differ. Geom. Appl. (IF 0.605) 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
Basic structures on derived critical loci Differ. Geom. Appl. (IF 0.605) 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
Anomaly formulas for the complex-valued analytic torsion on compact bordisms. Differ. Geom. Appl. 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