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.
ON THE STRUCTURE OF BESSE CONVEX CONTACT SPHERES
Radeschi, M
2022-01-01
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.
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