A characterization of Zoll Riemannian metrics on the 2-sphere

Marco Mazzucchelli; Stefan Suhr

doi:10.1112/blms.12200

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arXiv · 1711.11285

A characterization of Zoll Riemannian metrics on the 2-sphere

Marco Mazzucchelli·Stefan Suhr

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Abstract

The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2-sphere whose simple length spectrum consists of only one element L, any geodesic is simple closed with length L.

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Marco Mazzucchelli, Stefan Suhr. 2017-11-30. A characterization of Zoll Riemannian metrics on the 2-sphere. https://doi.org/10.1112/blms.12200

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