Higher systolic inequalities for 3-dimensional contact manifolds

Alberto Abbondandolo , Christian Lange , Marco Mazzucchelli (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We prove that Besse contact forms on closed connected 3-manifolds, that is, contact forms with a periodic Reeb flow, 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.

Domaines: Mathématiques [math]

Alberto Abbondandolo, Christian Lange, Marco Mazzucchelli. Higher systolic inequalities for 3-dimensional contact manifolds. Journal de l'École polytechnique — Mathématiques, 2022, 9, pp.807-851. ⟨10.5802/jep.195⟩. ⟨ensl-03357629⟩