Expansive dynamics and hyperbolic geometry |
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Authors: | Rafael O Ruggiero |
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Institution: | (1) Departamento de Matemática, Pontificia Universidade Católica do Rio de Janeiro, P.U.C., Rua Marquês de São Vicente, 225, 22453 Rio de Janeiro, Brasil |
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Abstract: | LetM be a compact Riemannian manifold with no conjugate points such that its geodesic flow is expansive. Then we show that the universal Riemannian covering ofM is a hyperbolic geodesic space according to the definition of M. Gromov. This allows us to extend a series of relevant geometric and topological properties of negatively curved manifolds toM and in particular, geometric group theory applies to the fundamental group ofM. |
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Keywords: | |
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