Systolic inequalities for S1-invariant contact forms in dimension three

TL;DR

This paper establishes a universal systolic inequality for S1-invariant contact forms on Seifert bundles with non-zero Euler number, linking the shortest Reeb orbit period to contact volume.

Contribution

It proves a new systolic inequality applicable to all S1-invariant contact forms on certain Seifert bundles, extending previous results in contact geometry.

Findings

Validates the inequality for all such contact forms

Links Reeb orbit period to contact volume in new settings

Applies to Seifert bundles with non-zero Euler number

Abstract

In contact geometry, a systolic inequality is a uniform upper bound on the shortest period of a closed Reeb orbit, in terms of the contact volume. We prove a general systolic inequality valid on Seifert bundles with non-zero Euler number for all contact forms that are invariant under the underlying circle action.