Open Access
Translator Disclaimer
2017 Characterizations of the round two-dimensional sphere in terms of closed geodesics
Lee Kennard, Jordan Rainone
Involve 10(2): 243-255 (2017). DOI: 10.2140/involve.2017.10.243

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.

Citation

Download Citation

Lee Kennard. Jordan Rainone. "Characterizations of the round two-dimensional sphere in terms of closed geodesics." Involve 10 (2) 243 - 255, 2017. https://doi.org/10.2140/involve.2017.10.243

Information

Received: 30 August 2015; Revised: 7 March 2016; Accepted: 25 March 2016; Published: 2017
First available in Project Euclid: 13 December 2017

zbMATH: 1352.53034
MathSciNet: MR3574299
Digital Object Identifier: 10.2140/involve.2017.10.243

Subjects:
Primary: 53C20 , 58E10

Keywords: closed geodesics , surface of revolution

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.10 • No. 2 • 2017
MSP
Back to Top