Characterizing Round Spheres Using Half-Geodesics
Differential Geometry
2022-06-08 v1
Abstract
A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.
Cite
@article{arxiv.1904.12080,
title = {Characterizing Round Spheres Using Half-Geodesics},
author = {Ian M Adelstein and Benjamin Schmidt},
journal= {arXiv preprint arXiv:1904.12080},
year = {2022}
}