Partially hyperbolic geodesic flows |
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Authors: | Fernando Carneiro Enrique Pujals |
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Affiliation: | 1. UERJ, R. São Francisco Xavier, 524, sala d6021 – Maracanã, Rio de Janeiro, RJ, cep 20550-013, Brazil;2. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, RJ, cep 22460-320, Brazil |
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Abstract: | We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, deforming the metric of a compact locally symmetric space of nonconstant negative curvature. Candidates for such an example as the product metric and locally symmetric spaces of nonpositive curvature with rank bigger than one are not partially hyperbolic. We prove that if a metric of nonpositive curvature has a partially hyperbolic geodesic flow, then its rank is one. Other obstructions to partial hyperbolicity of a geodesic flow are also analyzed. |
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