On the almost negatively curved 3-sphere

1988 ◽  
pp. 78-85 ◽  
Author(s):  
Peter Buser ◽  
Detlef Gromoll
Keyword(s):  
Negatively Curved

scholarly journals On quasiconvex subgroups of negatively curved groups

1997 ◽  
Vol 119 (2) ◽  
pp. 155-169 ◽  
Author(s):  
Rita Gitik
Keyword(s):  
Negatively Curved ◽  
Quasiconvex Subgroups

Double-Helix Supramolecular Nanofibers Assembled from Negatively Curved Nanographenes

2021 ◽  
Author(s):  
Kenta Kato ◽  
Kiyofumi Takaba ◽  
Saori Maki-Yonekura ◽  
Nobuhiko Mitoma ◽  
Yusuke Nakanishi ◽  
...  
Keyword(s):  
Double Helix ◽  
Negatively Curved

Gromov hyperbolicity of negatively curved Finsler manifolds

2011 ◽  
Vol 97 (3) ◽  
pp. 281-288 ◽  
Author(s):  
Yong Fang
Keyword(s):  
Gromov Hyperbolicity ◽  
Finsler Manifolds ◽  
Negatively Curved

scholarly journals A Lower Bound for the Remainder in Weyl's Law on Negatively Curved Surfaces

2007 ◽  
Vol 2007 ◽  
Author(s):  
Dmitry Jakobson ◽  
Iosif Polterovich ◽  
John A. Toth
Keyword(s):  
Lower Bound ◽  
Curved Surfaces ◽  
Weyl’S Law ◽  
Negatively Curved ◽  
Weyl's Law

Torus actions, maximality, and non-negative curvature

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Escher ◽  
Catherine Searle
Keyword(s):  
Negative Curvature ◽  
Torus Action ◽  
Maximal Symmetry ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Product Of Spheres ◽  
Rank Conjecture ◽  
Simply Connected ◽  
Symmetry Rank ◽  
Special Case

Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we show the Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.

Negatively Curved Geometry

2019 ◽  
pp. 23-48
Author(s):  
Anne Broise-Alamichel ◽  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Negatively Curved

scholarly journals Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution

2016 ◽  
Vol 102 (1) ◽  
pp. 37-66 ◽  
Author(s):  
Junehyuk Jung ◽  
Steve Zelditch
Keyword(s):  
Singular Points ◽  
Curved Surfaces ◽  
Nodal Domains ◽  
Negatively Curved

scholarly journals Cocycle superrigidity and bounded cohomology for negatively curved spaces

2004 ◽  
Vol 67 (3) ◽  
pp. 395-455 ◽  
Author(s):  
Nicolas Monod ◽  
Yehuda Shalom
Keyword(s):  
Bounded Cohomology ◽  
Curved Spaces ◽  
Negatively Curved

scholarly journals The singular terms in the fundamental matrix of crystal optics

2011 ◽  
Vol 467 (2133) ◽  
pp. 2663-2689 ◽  
Author(s):  
Peter Wagner
Keyword(s):  
Explicit Formula ◽  
Fundamental Matrix ◽  
Singular Part ◽  
Wave Surface ◽  
Crystal Optics ◽  
Cauchy Principal ◽  
Singular Terms ◽  
Negatively Curved ◽  
Principal Value ◽  
Positively Curved

We derive an explicit formula for the singular part of the fundamental matrix of crystal optics. It consists of a singularity remaining fixed at the origin x =0, of delta terms located on the positively curved parts of the wave surface, the well-known Fresnel surface and of a Cauchy principal value distribution on the negatively curved part of the wave surface.

On Flag Curvature of Homogeneous Randers Spaces

2013 ◽  
Vol 65 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Shaoqiang Deng ◽  
Zhiguang Hu
Keyword(s):  
Explicit Formula ◽  
Lie Group ◽  
Flag Curvature ◽  
Nilpotent Lie Group ◽  
Finsler Spaces ◽  
Rigidity Result ◽  
Randers Space ◽  
Negatively Curved

AbstractIn this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randersmetric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.

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