Geodesic
On the spectral characterization of Besse and Zoll Reeb flows
Ginzburg, Viktor L.1 ; Gürel, Başak Z.2 ; Mazzucchelli, Marco3
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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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 S1-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 :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.08.004
Classification : 53D10, 58E05, 53C22
Keywords: Closed Reeb orbits, Closed geodesics, Besse manifolds, Zoll manifolds

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 
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     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

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).