Riemannian manifolds with Anosov geodesic flow do not have conjugate points
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866917736821555200 |
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| author | Melo, Ítalo Romaña, Sergio |
| author_facet | Melo, Ítalo Romaña, Sergio |
| contents | This paper establishes a significant result concerning the absence of conjugate points in certain complete Riemannian manifolds. Specifically, we demonstrate that any complete non-compact manifold with curvature bounded below and an Anosov geodesic flow does not possess conjugate points. This resolves an open problem left by R. Mañé in [9] and subsequently highlighted by [7]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12898 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Riemannian manifolds with Anosov geodesic flow do not have conjugate points Melo, Ítalo Romaña, Sergio Dynamical Systems 37D40, 37C10, 53C22 This paper establishes a significant result concerning the absence of conjugate points in certain complete Riemannian manifolds. Specifically, we demonstrate that any complete non-compact manifold with curvature bounded below and an Anosov geodesic flow does not possess conjugate points. This resolves an open problem left by R. Mañé in [9] and subsequently highlighted by [7]. |
| title | Riemannian manifolds with Anosov geodesic flow do not have conjugate points |
| topic | Dynamical Systems 37D40, 37C10, 53C22 |
| url | https://arxiv.org/abs/2008.12898 |