A characterization of Zoll Riemannian metrics on the 2-sphere
Differential Geometry
2018-12-06 v2 Algebraic Topology
Geometric Topology
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.
Cite
@article{arxiv.1711.11285,
title = {A characterization of Zoll Riemannian metrics on the 2-sphere},
author = {Marco Mazzucchelli and Stefan Suhr},
journal= {arXiv preprint arXiv:1711.11285},
year = {2018}
}
Comments
11 pages, 1 figure. Version 2: added more details on Grayson's curve shortening flow