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arXiv · 1507.00414

Characterizations of the round two-dimensional sphere in terms of closed geodesics

Lee Kennard·Jordan Rainone
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Abstract

The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understood in the case of surfaces. For surfaces of revolution diffeomorphic to the sphere, a refinement of this problem was introduced by Borzellino, Jordan-Squire, Petrics, and Sullivan. In this article, we quantify their result by counting distinct geodesics of bounded length. In addition, we reframe these results to obtain a couple of characterizations of the round two-sphere.

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Lee Kennard, Jordan Rainone. 2015-07-02. Characterizations of the round two-dimensional sphere in terms of closed geodesics. https://doi.org/10.2140/involve.2017.10.243

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