# On the structure of Besse convex contact spheres

Abstract : We consider convex contact spheres $Y$ all of whose Reeb orbits are closed. Any such $Y$ admits a stratification by the periods of closed Reeb orbits. We show that $Y$ "resembles" a contact ellipsoid: any stratum of $Y$ is an integral homology sphere, and the sequence of Ekeland-Hofer spectral invariants of $Y$ coincides with the full sequence of action values, each one repeated according to its multiplicity.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-ens-lyon.archives-ouvertes.fr/ensl-03053467
Contributor : Marco Mazzucchelli <>
Submitted on : Friday, December 11, 2020 - 9:13:34 AM
Last modification on : Saturday, December 12, 2020 - 3:30:24 AM

### Identifiers

• HAL Id : ensl-03053467, version 1
• ARXIV : 2012.05389

### Citation

Marco Mazzucchelli, Marco Radeschi. On the structure of Besse convex contact spheres. 2020. ⟨ensl-03053467⟩

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