On the spectral characterization of Besse and Zoll Reeb flows

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-01 DOI:10.1016/j.anihpc.2020.08.004

Viktor L. Ginzburg , Başak Z. Gürel , Marco Mazzucchelli

引用次数: 9

Abstract

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian unit tangent bundles in terms of $S^{1}$ -equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.

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Besse和Zoll Reeb流的谱特征

当一个闭合接触流形的所有Reeb轨道都闭合时，它被称为Besse，当它们具有相同的最小周期时，它被称为Zoll。本文用s1等变谱不变量给出了凸接触球和黎曼单位切线束的贝塞接触形式的表征。此外，对于辛向量空间的受限接触型超曲面，我们通过Ekeland-Hofer能力给出了Besse性质的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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