Riemannian manifolds with Anosov geodesic flow do not have conjugate points

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. Mañé in [9] and subsequently highlighted by [7].

arXiv commentWe 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)