Rigidity of Hamenstädt metrics of Anosov flows

Yong Fang

doi:10.3934/dcds.2016.36.1271

Article Contents

2016, Volume 36, Issue 3: 1271-1278. Doi: 10.3934/dcds.2016.36.1271

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Rigidity of Hamenstädt metrics of Anosov flows

Yong Fang^1,

1.
Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex

Received: December 31, 2014

Revised: April 30, 2015

Published: May 2017

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Abstract

Let $\varphi$ be a $C^\infty$ transversely symplectic topologically mixing Anosov flow such that $dim E^{su}\geq 2$. We suppose that the weak distributions of $\varphi$ are $C^1$. If the length Hamenstädt metrics of $\varphi$ are sub-Riemannian then we prove that the weak distributions of $\varphi$ are necessarily $C^\infty$. Combined with our previous rigidity result in [5] we deduce the classification of such Anosov flows with $C^1$ weak distributions provided that the length Hamenstädt metrics are sub-Riemannian.

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Mathematics Subject Classification: Primary: 37A35, 34D20; Secondary: 37D35, 37D40.

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References

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