Higher systolic inequalities for 3-dimensional contact manifolds

TL;DR

This paper proves that Besse contact forms on closed 3-manifolds locally maximize certain higher systolic ratios, extending previous results for Zoll contact forms with free circle actions.

Contribution

It establishes that Besse contact forms are local maximizers of higher systolic ratios, generalizing earlier results for Zoll contact forms.

Findings

Besse contact forms are local maximizers of higher systolic ratios.

Extension of results from Zoll to Besse contact forms.

Provides new insights into systolic inequalities in contact geometry.

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.