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arXiv · 1809.08689

A min-max characterization of Zoll Riemannian metrics

Marco Mazzucchelli·Stefan Suhr
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Abstract

We characterize 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.

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Marco Mazzucchelli, Stefan Suhr. 2018-10-25. A min-max characterization of Zoll Riemannian metrics. https://doi.org/10.1017/s0305004121000311

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