JournalsaihpcVol. 38, No. 3pp. 549–576

On the spectral characterization of Besse and Zoll Reeb flows

  • Viktor L. Ginzburg

    Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA

  • Başak Z. Gürel

    Department of Mathematics, UCF, Orlando, FL 32816, USA

  • Marco Mazzucchelli

    CNRS, UMPA, École Normale Supérieure de Lyon, 69364 Lyon, France
On the spectral characterization of Besse and Zoll Reeb flows cover

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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 -equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.

Cite this article

Viktor L. Ginzburg, Başak Z. Gürel, Marco Mazzucchelli, On the spectral characterization of Besse and Zoll Reeb flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 549–576

DOI 10.1016/J.ANIHPC.2020.08.004