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arXiv · 1904.12080

Characterizing Round Spheres Using Half-Geodesics

Ian M Adelstein·Benjamin Schmidt
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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 note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

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Ian M Adelstein, Benjamin Schmidt. 2019-04-27. Characterizing Round Spheres Using Half-Geodesics. https://doi.org/10.1073/pnas.1907226116

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