%0 Journal Article
%T Rigidity properties of Anosov optical hypersurfaces
%A Nurlan S. Dairbekov
%A Gabriel P. Paternain
%J Mathematics
%D 2005
%I arXiv
%X We consider an optical hypersurface $\Sigma$ in the cotangent bundle $\tau:T^*M\to M$ of a closed manifold $M$ endowed with a twisted symplectic structure. We show that if the characteristic foliation of $\Sigma$ is Anosov, then a smooth 1-form $\theta$ on $M$ is exact if and only $\tau^*\theta$ has zero integral over every closed characteristic of $\Sigma$. This result is derived from a related theorem about magnetic flows which generalizes our work in \cite{DP}. Other rigidity issues are also discussed.
%U http://arxiv.org/abs/math/0508316v1