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A dynamical-geometric characterization of the geodesic flows of negatively curved locally symmetric spaces

Published online by Cambridge University Press:  03 July 2014

YONG FANG
YONG FANG*
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France email yfang@u-cergy.fr
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Abstract

In this paper we prove the following rigidity result: let ${\it\varphi}$ be a $C^{\infty }$ topologically mixing transversely symplectic Anosov flow. If (i) its weak stable and weak unstable distributions are $C^{\infty }$ and (ii) its Hamenstädt metrics are sub-Riemannian, then up to finite covers and a constant change of time scale, ${\it\varphi}$ is $C^{\infty }$ flow conjugate to the geodesic flow of a closed locally symmetric Riemannian space of rank one.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2094 - 2113
Copyright
© Cambridge University Press, 2014 

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