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Morse-Smale characteristic foliations and convexity in contact manifolds
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-06-18 , DOI: 10.1090/proc/15484 Joseph Breen
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-06-18 , DOI: 10.1090/proc/15484 Joseph Breen
Abstract:We generalize a result of Giroux which says that a closed surface in a contact $3$-manifold with Morse-Smale characteristic foliation is convex. Specifically, we show that the result holds in contact manifolds of arbitrary dimension. As an application, we show that a particular closed hypersurface introduced by A. Mori is $C^{\infty }$-close to a convex hypersurface.
中文翻译:
接触流形中的 Morse-Smale 特征叶面和凸度
摘要:我们概括了 Giroux 的结果,该结果表明,具有 Morse-Smale 特征叶理的接触 $3$-流形中的闭合曲面是凸面。具体来说,我们表明该结果适用于任意维度的接触流形。作为一个应用,我们展示了由 A. Mori 引入的特定封闭超曲面是 $C^{\infty }$-接近凸超曲面。
更新日期:2021-07-27
中文翻译:
接触流形中的 Morse-Smale 特征叶面和凸度
摘要:我们概括了 Giroux 的结果,该结果表明,具有 Morse-Smale 特征叶理的接触 $3$-流形中的闭合曲面是凸面。具体来说,我们表明该结果适用于任意维度的接触流形。作为一个应用,我们展示了由 A. Mori 引入的特定封闭超曲面是 $C^{\infty }$-接近凸超曲面。