Characterizing round spheres using half-geodesics.

Adelstein, Ian M; Schmidt, Benjamin · Proc Natl Acad Sci U S A · 2019

basic_science · Level V

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