Geodesic
On the spectral characterization of Besse and Zoll Reeb flows
Ginzburg, Viktor L.1 ; Gürel, Başak Z.2 ; Mazzucchelli, Marco3
1a Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA
2b Department of Mathematics, UCF, Orlando, FL 32816, USA
3c 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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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

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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).