Une forme de contact est dite de type Besse si son flot de Reeb est périodique. On prouve que les formes de contact de type Besse sur les variétés connexes fermées de dimension sont les maximiseurs locaux de certains rapports systoliques d’ordre supérieur. Notre résultat étend des théorèmes antérieurs pour les formes de contact de type Zoll, c’est-à-dire les formes de contact dont le flot de Reeb définit une action libre du cercle.
A contact form is called Besse when the associated Reeb flow is periodic. We prove that Besse contact forms on closed connected -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.
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Keywords: Systolic inequalities, Besse contact forms, Seifert fibrations, Calabi homomorphism
Mot clés : Inégalités systoliques, formes de contact de type Besse, fibrations de Seifert, homomorphisme de Calabi
@article{JEP_2022__9__807_0, author = {Abbondandolo, Alberto and Lange, Christian and Mazzucchelli, Marco}, title = {Higher systolic inequalities for 3-dimensional~contact manifolds}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {807--851}, publisher = {Ecole polytechnique}, volume = {9}, year = {2022}, doi = {10.5802/jep.195}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jep.195/} }
TY - JOUR AU - Abbondandolo, Alberto AU - Lange, Christian AU - Mazzucchelli, Marco TI - Higher systolic inequalities for 3-dimensional contact manifolds JO - Journal de l’École polytechnique — Mathématiques PY - 2022 SP - 807 EP - 851 VL - 9 PB - Ecole polytechnique UR - http://archive.numdam.org/articles/10.5802/jep.195/ DO - 10.5802/jep.195 LA - en ID - JEP_2022__9__807_0 ER -
%0 Journal Article %A Abbondandolo, Alberto %A Lange, Christian %A Mazzucchelli, Marco %T Higher systolic inequalities for 3-dimensional contact manifolds %J Journal de l’École polytechnique — Mathématiques %D 2022 %P 807-851 %V 9 %I Ecole polytechnique %U http://archive.numdam.org/articles/10.5802/jep.195/ %R 10.5802/jep.195 %G en %F JEP_2022__9__807_0
Abbondandolo, Alberto; Lange, Christian; Mazzucchelli, Marco. Higher systolic inequalities for 3-dimensional contact manifolds. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 807-851. doi : 10.5802/jep.195. http://archive.numdam.org/articles/10.5802/jep.195/
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