Partially hyperbolic geodesic flows

Carneiro, Fernando; Pujals, Enrique

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 5, pp. 985-1014.

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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