Besse和Zoll Reeb流的谱特征

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

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引用次数: 9

摘要

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。

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On the spectral characterization of Besse and Zoll Reeb flows

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.