Contributions to the study of Anosov geodesic flows in non-compact manifolds

Abstract

In this paper, we study the relations between curvature and Anosov geodesic flow. More specifically, we prove that when the geodesic flow of a complete manifold without conjugate points is of the Anosov type, then the average of the sectional curvature in tangent planes along geodesics is negative and uniformly away from zero. Moreover, if a surface has no focal points, then the latter condition is sufficient to obtain that the geodesic flow is of Anosov type.