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

2023/04/20 by Alexander Cantoral, Sergio Romaña, Cantoral, Alexander +1 · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2304.10606

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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• Curvature Rigidity Through Level Sets of Lyapunov Exponents in Geodesic Flows

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