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arXiv · 2008.12898

Riemannian manifolds with Anosov geodesic flow do not have conjugate points

Ítalo Melo·Sergio Romaña
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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].

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Ítalo Melo, Sergio Romaña. 2020-08-29. Riemannian manifolds with Anosov geodesic flow do not have conjugate points. https://arxiv.org/abs/2008.12898

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