JournalsaihpcVol. 31, No. 5pp. 985–1014

Partially hyperbolic geodesic flows

  • Fernando Carneiro

    UERJ, R. São Francisco Xavier, 524, sala d6021 – Maracanã, Rio de Janeiro, RJ, cep 20550-013, Brazil

  • Enrique Pujals

    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.

Cite this article

Fernando Carneiro, Enrique Pujals, Partially hyperbolic geodesic flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, pp. 985–1014

DOI 10.1016/J.ANIHPC.2013.07.009