A Note on Anosov flows of non-compact Riemannian manifolds

TL;DR

This paper establishes a condition on non-compact Riemannian manifolds that guarantees the absence of conjugate points when the geodesic flow is Anosov under the Sasaki metric.

Contribution

It introduces a new condition linking Anosov geodesic flows to the geometric property of having no conjugate points on non-compact manifolds.

Findings

Identifies a specific condition for non-compact manifolds with Anosov geodesic flow

Shows that this condition implies no conjugate points

Provides insights into the geometric structure of such manifolds

Abstract

In this note we formulate a condition for complete, connected and non-compact Riemannian manifolds which implies no conjugate points in case that the geodesic flow is Anosov with respect to the Sasaki metric.