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arXiv · 1810.09998

Contributions to the study of Anosov Geodesic Flows in Non-Compact Manifolds

Ítalo Melo·Sergio Romaña
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Abstract

In this paper we prove that if the geodesic flow of a {compact or non-compact} complete manifold without conjugate points is of the Anosov type, then the average of the integral of the sectional curvature along the geodesic is negative and away from zero from a uniform time. Moreover, in dimension two, if the manifold has no focal points, then this condition is sufficient to obtain that the geodesic flow is of Anosov type. This sufficient condition will also be used to construct new examples of non-compact surfaces whose geodesic flow is of the Anosov type.

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Ítalo Melo, Sergio Romaña. 2018-10-23. Contributions to the study of Anosov Geodesic Flows in Non-Compact Manifolds. https://arxiv.org/abs/1810.09998

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