Gromov-hyperbolicity and transitivity of geodesic flows in n-dimensional Finsler manifolds
| Autor: | Alessandro Gaio Chimenton, José Barbosa Gomes, Rafael O. Ruggiero |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Transitive relation N dimensional Geodesic 010102 general mathematics Visibility (geometry) Conjugate points Extension (predicate logic) 01 natural sciences Computational Theory and Mathematics 0103 physical sciences Geodesic flow Mathematics::Metric Geometry Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology Finsler manifold 0101 mathematics Mathematics::Symplectic Geometry Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 68:101588 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2019.101588 |
| Popis: | 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 δ-hyperbolicity and Eberlein's visibility, and study their consequences. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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