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# On the spectral characterization of Besse and Zoll Reeb flows

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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Preprints, Working Papers, ...
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-02352680
Contributor : Marco Mazzucchelli Connect in order to contact the contributor
Submitted on : Thursday, November 7, 2019 - 1:01:28 AM
Last modification on : Thursday, March 5, 2020 - 3:30:28 PM

### Identifiers

• HAL Id : ensl-02352680, version 1
• ARXIV : 1909.03310

### Citation

Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. On the spectral characterization of Besse and Zoll Reeb flows. 2019. ⟨ensl-02352680⟩

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