Gromov-hyperbolicity and transitivity of geodesic flows in n-dimensional Finsler manifolds

被引：2

作者：

Chimenton, Alessandro Gaio ^{[1
]}

Gomes, Jose Barbosa ^{[2
]}

Ruggiero, Rafael O. ^{[3
]}

机构：

[1] Univ Fed Fluminense, Dept Matemat, Campus Aterrado, BR-27213145 Volta Redonda, RJ, Brazil

[2] Univ Fed Juiz de Fora, Dept Matemat, BR-36036900 Juiz De Fora, MG, Brazil

[3] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, BR-22453900 Rio De Janeiro, RJ, Brazil

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2020年 / 68卷

关键词：

Finsler metric; Geodesic flow; Transitivity; Gromov-hyperbolicity; COMPACT SURFACES; GENUS;

D O I：

10.1016/j.difgeo.2019.101588

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the geodesic flow of a compact Finsler manifold without conjugate points is transitive provided that the universal covering satisfies the uniform Finsler visibility condition. This result is a nontrivial extension of a well known theorem due to Eberlein for Riemannian manifolds. For doing so, we introduce suitable Finsler versions of the concepts of Gromov's delta-hyperbolicity and Eberlein's visibility, and study their consequences. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：30

共 50 条

[1] Gromov hyperbolicity of negatively curved Finsler manifolds
Fang, Yong
ARCHIV DER MATHEMATIK, 2011, 97 (03) : 281 - 288
[2] Gromov hyperbolicity of negatively curved Finsler manifolds
Yong Fang
Archiv der Mathematik, 2011, 97 : 281 - 288
[3] CENTRAL LIMIT THEOREM FOR GEODESIC FLOWS ON N-DIMENSIONAL MANIFOLDS OF NEGATIVE CURVATURE
RATNER, M
ISRAEL JOURNAL OF MATHEMATICS, 1973, 16 (02) : 181 - 197
[4] On Finsler manifolds with hyperbolic geodesic flows
Fang, Yong
ARCHIV DER MATHEMATIK, 2021, 117 (02) : 233 - 239
[5] On Finsler manifolds with hyperbolic geodesic flows
Yong Fang
Archiv der Mathematik, 2021, 117 : 233 - 239
[6] The transitivity of geodesic flows on rank 1 manifolds without focal points
Liu, Fei
Zhu, Xiongfeng
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2018, 60 : 49 - 53
[7] TRANSITIVITY OF FINSLER GEODESIC FLOWS OF COMPACT SURFACES WITHOUT CONJUGATE POINTS AND HIGHER GENUS, AND APPLICATIONS TO FINSLER RIGIDITY PROBLEMS
Chimenton, Alessandro G.
Comes, Jose Barbosa
Ruggiero, Rafael O.
HOUSTON JOURNAL OF MATHEMATICS, 2015, 41 (02): : 523 - 551
[8] The Hausdorff Measure on n-Dimensional Manifolds in ℝm and n-Dimensional Variations
Potepun A.V.
Journal of Mathematical Sciences, 2019, 243 (6) : 917 - 921
[9] The geodesic complexity of n-dimensional Klein bottles
Davis, Donald M.
Recio-Mitter, David
NEW YORK JOURNAL OF MATHEMATICS, 2021, 27 : 296 - 318
[10] Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk
Giambo, Roberto
Giannoni, Fabio
Piccione, Paolo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (02) : 290 - 337

← 1 2 3 4 5 →