Riemannian manifolds with Anosov geodesic flow do not have conjugate points
Dynamical Systems
2024-07-31 v3
Abstract
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. Ma\~n\'e in [9] and subsequently highlighted by [7].
Keywords
Cite
@article{arxiv.2008.12898,
title = {Riemannian manifolds with Anosov geodesic flow do not have conjugate points},
author = {Ítalo Melo and Sergio Romaña},
journal= {arXiv preprint arXiv:2008.12898},
year = {2024}
}
Comments
We have added Theorem 4.1 and Lemma 4.10 with a precise estimate and revised the proof of Lemma 4.9 (now Lemma 4.11)