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

[41] Reduction of Volume-preserving Flows on an n-dimensional Manifold
Yong-ai Zheng
De-bin Huang
Zeng-rong Liu
Acta Mathematicae Applicatae Sinica, 2003, 19 (1) : 129 - 134
[42] N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS
Lienhardt, Pascal
INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS, 1994, 4 (03) : 275 - 324
[43] BOCHER-TYPE THEOREM ON N-DIMENSIONAL MANIFOLDS WITH CONICAL METRIC
Li, Jiayu
Wan, Fangshu
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (10) : 4527 - 4538
[44] ANALYTIC SHEAF COHOMOLOGY GROUPS OF DIMENSION N OF N-DIMENSIONAL NONCOMPACT COMPLEX MANIFOLDS
SIU, YT
PACIFIC JOURNAL OF MATHEMATICS, 1969, 28 (02) : 407 - &
[45] FRACTION-QUADRATIC INTEGRAL OF GEODESIC LINES IN N-DIMENSIONAL SPACES OF AFFINE CONNECTIVITY
PISSAREVA, NM
DOKLADY AKADEMII NAUK SSSR, 1956, 108 (02): : 198 - 200
[46] ANOSOV-FLOWS WITH SMOOTH FOLIATIONS AND RIGIDITY OF GEODESIC-FLOWS ON 3-DIMENSIONAL MANIFOLDS OF NEGATIVE CURVATURE
FERES, R
KATOK, A
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 : 657 - 670
[47] The intersection angles between N-dimensional stable and unstable manifolds in 2N-dimensional symplectic mappings
Hirata, Y
Nozaki, K
Konishi, T
PROGRESS OF THEORETICAL PHYSICS, 1999, 102 (03): : 701 - 706
[48] Smooth and analytic actions of SL(n,R)and SL(n,Z)on closed n-dimensional manifolds
Fisher, David
Melnick, Karin
KYOTO JOURNAL OF MATHEMATICS, 2024, 64 (04) : 873 - 904
[49] CURVATURE INVARIANTS ASSOCIATED WITH SETS OF N FUNDAMENTAL FORMS OF HYPERSURFACES OF N-DIMENSIONAL RIEMANNIAN MANIFOLDS
RUND, H
TENSOR, 1971, 22 (02): : 163 - &
[50] BACKLUND THEOREM FOR N-DIMENSIONAL SUB-MANIFOLDS OF R2N-1
TENENBLAT, K
TERNG, CL
ANNALS OF MATHEMATICS, 1980, 111 (03) : 477 - 490

← 1 2 3 4 5 →