American Institute of Mathematical Sciences

March  2016, 36(3): 1271-1278. doi: 10.3934/dcds.2016.36.1271

Rigidity of Hamenstädt metrics of Anosov flows

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

Received  January 2015 Revised  May 2015 Published  August 2015

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.
Citation: Yong Fang. Rigidity of Hamenstädt metrics of Anosov flows. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1271-1278. doi: 10.3934/dcds.2016.36.1271
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