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A min-max characterization of Zoll Riemannian metrics
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.8 ) Pub Date : 2021-04-29 , DOI: 10.1017/s0305004121000311
MARCO MAZZUCCHELLI 1 , STEFAN SUHR 2
Affiliation  

We characterise the Zoll Riemannian metrics on a given simply connected spin closed manifold as those Riemannian metrics for which two suitable min-max values in a finite dimensional loop space coincide. We also show that on odd dimensional Riemannian spheres, when certain pairs of min-max values in the loop space coincide, every point lies on a closed geodesic.



中文翻译:

Zoll 黎曼度量的最小-最大表征

我们将给定简单连接自旋封闭流形上的 Zoll Riemannian 度量描述为那些在有限维环空间中两个合适的 min-max 值重合的黎曼度量。我们还表明,在奇数维黎曼球体上,当循环空间中的某些最小-最大值对重合时,每个点都位于闭合测地线上。

更新日期:2021-04-29
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