On the spectral characterization of Besse and Zoll Reeb flows
Symplectic Geometry
2021-03-09 v2 Differential Geometry
Dynamical Systems
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 Euclidean spaces, we give a sufficient condition for the Besse property via the Ekeland-Hofer capacities.
Keywords
Cite
@article{arxiv.1909.03310,
title = {On the spectral characterization of Besse and Zoll Reeb flows},
author = {Viktor L. Ginzburg and Basak Z. Gurel and Marco Mazzucchelli},
journal= {arXiv preprint arXiv:1909.03310},
year = {2021}
}
Comments
33 pages; version 2: minor corrections