三维接触流形的高收缩不等式

Journal de l’École polytechnique — Mathématiques Pub Date : 2021-07-26 DOI:10.5802/jep.195

Alberto Abbondandolo, Christian Lange, M. Mazzucchelli

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引用次数: 2

摘要

当关联的Reeb流是周期性的时，联系表单称为Besse。证明了闭连通3流形上的贝塞接触形式是具有合适的高收缩比的局部最优形式。我们的结果扩展了之前针对Zoll接触表单的结果，也就是说，接触表单的Reeb流定义了一个自由圆动作。

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Higher systolic inequalities for 3-dimensional contact manifolds

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.

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Journal de l’École polytechnique — Mathématiques

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