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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关于Besse和Zoll Reeb流的光谱表征

闭合的接触歧管在其所有的Reeb轨道都闭合时称为Besse，在它们的最小周期相同时称为Zoll。在本文中，我们提供了凸接触球体和黎曼单元切线束的贝西接触形式的特征，用${\mathrm{小号}}^{\mathrm{1个}}$等谱谱不变式。此外，对于辛矢量空间的受限接触型超曲面，我们通过Ekeland-Hofer容量为Besse属性提供了充分条件。