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Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2020

## On the spectral characterization of Besse and Zoll Reeb flows

Viktor L. Ginzburg
• Function : Author
Basak Z. Gurel
• Function : Author
Marco Mazzucchelli

#### 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.

### Dates and versions

ensl-02352680 , version 1 (10-03-2023)

### Licence

Attribution - NonCommercial - CC BY 4.0

### Identifiers

• HAL Id : ensl-02352680 , version 1
• ARXIV :
• DOI :
• PII :

### Cite

Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. On the spectral characterization of Besse and Zoll Reeb flows. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, ⟨10.1016/j.anihpc.2020.08.004⟩. ⟨ensl-02352680⟩

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