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.

arXiv comment29 pages; final version: we added a reference to Ustilovsky's construction of exotic Besse contact spheres. To appear in Trans. Amer. Math. Soc

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• On the spectral characterization of Besse and Zoll Reeb flows
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Cited by in corpus (3)

• Surfaces of section for Seifert fibrations
• Higher systolic inequalities for 3-dimensional contact manifolds
• Convex bodies with all characteristics planar