Dynamics and Topology of Conformally Anosov Contact 3-Manifolds

Surena Hozoori

doi:10.1016/j.difgeo.2020.101679

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arXiv · 1908.07990

Dynamics and Topology of Conformally Anosov Contact 3-Manifolds

Surena Hozoori

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Abstract

We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show $\mathbb{S}^3$ does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a contact structure implying that a Reeb field is Anosov. From this we can give curvature conditions on a metric compatible with a contact structure that implies universal tightness of the contact structure among other things.

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Surena Hozoori. 2019-08-21. Dynamics and Topology of Conformally Anosov Contact 3-Manifolds. https://doi.org/10.1016/j.difgeo.2020.101679

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