Cocompact Cat(0) Spaces Are Almost Geodesically Complete
نویسنده
چکیده
Let M be a Hadamard manifold, that is, a complete simply connected riemannian manifold with non-positive sectional curvatures. Then every geodesic segment α : [0, a] → M from α(0) to α(a) can be extended to a geodesic ray α : [0,∞) → M . We say then that the Hadamard manifold M is geodesically complete. Note that, in this case, all geodesic rays are proper maps. CAT(0) spaces are generalizations of Hadamard manifolds. For a CAT(0) space X, all geodesic rays α : [0,∞) → X are proper maps but, in general, X is not geodesically complete. The following definition of almost geodesic completeness was suggested by M. Mihalik:
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