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.

arXiv comment41 pages, 1 figure; version 2: minor corrections; to appear in Journal de l'École polytechnique - Mathématiques

References in corpus (11)

• The Seiberg-Witten equations and the Weinstein conjecture
• Transverse contact structures on Seifert 3-manifolds
• Sharp systolic inequalities for Reeb flows on the three-sphere
• A Boothby-Wang theorem for Besse contact manifolds
• The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed
• What does a vector field know about volume?
• On the structure of Besse convex contact spheres
• Surfaces of section for Seifert fibrations
• A local contact systolic inequality in dimension three
• On the local systolic optimality of Zoll contact forms
• Sharp systolic inequalities for rotationally symmetric 2-orbifolds