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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
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.
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- © Cambridge University Press, 2014