Contributions to the study of Anosov Geodesic Flows in Non-Compact Manifolds. (arXiv:1810.09998v1 [math.DS])

In this paper we prove that when the geodesic flow of a compact or non-compact complete manifold without conjugate points is of the Anosov type, then the average along of the sectional curvature in planes tangent to the geodesic is negative away from zero for some uniform time. Moreover, in dimension two, if the manifold has no focal points, then the latter condition is sufficient to obtain that the geodesic flow is of Anosov type. 查看全文>>