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

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