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arXiv · 1909.03310

On the spectral characterization of Besse and Zoll Reeb flows

Viktor L. Ginzburg·Basak Z. Gurel·Marco Mazzucchelli
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Abstract

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian unit tangent bundles in terms of $S^1$-equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic Euclidean spaces, we give a sufficient condition for the Besse property via the Ekeland-Hofer capacities.

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Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. 2019-09-07. On the spectral characterization of Besse and Zoll Reeb flows. https://doi.org/10.1016/j.anihpc.2020.08.004

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