English

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 S1S^1-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