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.
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