Answer by Neal for The number of geodesics of a complete Riemann manifold...
This answer is by AnonymousCoward from the comments. I am posting it as an answer for completeness' sake.We have $M$ a non-simply connected complete Riemannian manifold with nonpositive sectional...
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There is a theorem of Cartan which states that if $M$ is a simply connected, complete Riemann manifold, and that the sectional curvature is everywhere $\leq 0$, then any two points of M are joined by a...
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