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.
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.
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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
Alberto Abbondandolo 1; Christian Lange 2; Marco Mazzucchelli 3
@article{JEP_2022__9__807_0, author = {Alberto Abbondandolo and Christian Lange and Marco Mazzucchelli}, 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 = {https://jep.centre-mersenne.org/articles/10.5802/jep.195/} }
TY - JOUR AU - Alberto Abbondandolo AU - Christian Lange AU - Marco Mazzucchelli 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 - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.195/ DO - 10.5802/jep.195 LA - en ID - JEP_2022__9__807_0 ER -
%0 Journal Article %A Alberto Abbondandolo %A Christian Lange %A Marco Mazzucchelli %T Higher systolic inequalities for 3-dimensional contact manifolds %J Journal de l’École polytechnique — Mathématiques %D 2022 %P 807-851 %V 9 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.195/ %R 10.5802/jep.195 %G en %F JEP_2022__9__807_0
Alberto Abbondandolo; Christian Lange; Marco Mazzucchelli. Higher systolic inequalities for 3-dimensional contact manifolds. Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 807-851. doi : 10.5802/jep.195. https://jep.centre-mersenne.org/articles/10.5802/jep.195/
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