Preprint A716/2012
Partially hyperbolic geodesic flows

Enrique Pujals | Carneiro, Fernando

**Keywords: **
geodesic flows | partial hyperbolicity | deformation of metrics

We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, changing the metric of a compact locally symmetric space of nonconstant negative curvature. We also show that candidates for such example as the product metric and locally symmetric spaces of nonpositive curvature with rank bigger than one are not partially hyperbolic. We also prove that if a metric of nonpositive curvature is not a Riemannian product and its geodesic flow is partially hyperbolic, then its rank is one. Other obstructions to partial hyperbolicity of a geodesic flow are also analyzed.