Partially hyperbolic geodesic flows
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, p. 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.

@article{AIHPC_2014__31_5_985_0,
author = {Carneiro, Fernando and Pujals, Enrique},
title = {Partially hyperbolic geodesic flows},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {31},
number = {5},
year = {2014},
pages = {985-1014},
doi = {10.1016/j.anihpc.2013.07.009},
zbl = {1298.53089},
mrnumber = {3258363},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2014__31_5_985_0}
}
Carneiro, Fernando; Pujals, Enrique. Partially hyperbolic geodesic flows. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, pp. 985-1014. doi : 10.1016/j.anihpc.2013.07.009. http://www.numdam.org/item/AIHPC_2014__31_5_985_0/

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