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arXiv · 2304.10606

Geometric conditions to obtain Anosov geodesic flow in non-compact manifolds

Alexander Cantoral·Sergio Romaña
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Abstract

Let $(M, g)$ be a complete Riemannian manifold without focal points and curvature bounded below. We prove that when the average of the sectional curvature in tangent planes along geodesics is negative and uniformly away from zero, then the geodesic flow is of Anosov type. We use this result to construct a non-compact manifold of non-positive curvature with the geodesic flow of Anosov type.

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Alexander Cantoral, Sergio Romaña. 2023-04-20. Geometric conditions to obtain Anosov geodesic flow in non-compact manifolds. https://arxiv.org/abs/2304.10606

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