Higher systolic inequalities for 3-dimensional contact manifolds

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.

41 pages, 1 figure; version 2: minor corrections; to appear in Journal de l'École polytechnique - Mathématiques

References in corpus (4)

• On the structure of Besse convex contact spheres
• Surfaces of section for Seifert fibrations
• A local contact systolic inequality in dimension three
• Sharp systolic inequalities for rotationally symmetric 2-orbifolds