Rigidity properties of Anosov optical hypersurfaces

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We consider an optical hypersurface $Σ$ in the cotangent bundle $τ:T^*M\to M$ of a closed manifold $M$ endowed with a twisted symplectic structure. We show that if the characteristic foliation of $Σ$ is Anosov, then a smooth 1-form $θ$ on $M$ is exact if and only $τ^*θ$ has zero integral over every closed characteristic of $Σ$. This result is derived from a related theorem about magnetic flows which generalizes our work in \cite{DP}. Other rigidity issues are also discussed.

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Dynamical Systems, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/76057

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0508316
 http://arxiv.org/abs/math/0508316

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arXiv