On the spectral characterization of Besse and Zoll Reeb flows

Ginzburg, Viktor L.; Gürel, Başak Z.; Mazzucchelli, Marco

doi:10.1016/j.anihpc.2020.08.004

Ginzburg, Viktor L.¹ ; Gürel, Başak Z.² ; Mazzucchelli, Marco ³

¹ a Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA
² b Department of Mathematics, UCF, Orlando, FL 32816, USA
³ c CNRS, UMPA, École Normale Supérieure de Lyon, 69364 Lyon, France

Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 549-576.

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Résumé

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 vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.

Reçu le : 2019-09-07
Révisé le : 2020-03-22
Accepté le : 2020-08-07

MR Zbl

DOI : 10.1016/j.anihpc.2020.08.004

Classification : 53D10, 58E05, 53C22
Mots-clés : Closed Reeb orbits, Closed geodesics, Besse manifolds, Zoll manifolds

Affiliations des auteurs :

Ginzburg, Viktor L. ¹ ; Gürel, Başak Z. ² ; Mazzucchelli, Marco ³

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     title = {On the spectral characterization of {Besse} and {Zoll} {Reeb} flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Ginzburg, Viktor L.; Gürel, Başak Z.; Mazzucchelli, Marco. On the spectral characterization of Besse and Zoll Reeb flows. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 549-576. doi : 10.1016/j.anihpc.2020.08.004. http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.004/

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Cité par Sources :

This work was partially supported by the NSF Grant DMS-1440140 via MSRI (BG and MM), the NSF CAREER award DMS-1454342 (BG), and by Simons Foundation Collaboration Grant 581382 (VG).