Characterizing round spheres using half-geodesics [Mathematics]

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 paper establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

Source: Proceedings of the National Academy of Sciences - July 15, 2019 Category: Science Authors: Ian M. Adelstein, Benjamin Schmidt Tags: Physical Sciences Source Type: research