English

Higher systolic inequalities for 3-dimensional contact manifolds

Symplectic Geometry 2022-05-18 v2 Differential Geometry Dynamical Systems

Abstract

A contact form is called Besse when the associated Reeb flow is periodic. We prove that Besse contact forms on closed connected 3-manifolds are the local maximizers of suitable higher systolic ratios. Our result extends earlier ones for Zoll contact forms, that is, contact forms whose Reeb flow defines a free circle action.

Keywords

Cite

@article{arxiv.2107.12138,
  title  = {Higher systolic inequalities for 3-dimensional contact manifolds},
  author = {Alberto Abbondandolo and Christian Lange and Marco Mazzucchelli},
  journal= {arXiv preprint arXiv:2107.12138},
  year   = {2022}
}

Comments

41 pages, 1 figure; version 2: minor corrections; to appear in Journal de l'\'Ecole polytechnique - Math\'ematiques