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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The visibility axiom on a Hadamard manifold whose geodesic flow is of Anosov type


Author: Tetsuo Ukai
Journal: Proc. Amer. Math. Soc. 104 (1988), 577-583
MSC: Primary 53C25; Secondary 53C22, 58F17
MathSciNet review: 962831
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Abstract: For a Hadamard manifold $ M$, the set of points at infinity $ M(\infty )$ is defined. If the geodesic flow on the unit tangent bundle of $ M$ is of Anosov type, then with a certain curvature condition $ M$ satisfies the Visibility Axiom. To prove this result, we use the Tits metric on $ M(\infty )$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962831-3
PII: S 0002-9939(1988)0962831-3
Keywords: Hadamard manifold, geodesic flow, Anosov flow, Visibility Axiom, Tits metric, Busemann function, horosphere
Article copyright: © Copyright 1988 American Mathematical Society