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Characterizations
of the round two-dimensional sphere in terms of closed
geodesics
Lee Kennard and Jordan Rainone
Vol. 10 (2017), No. 2, 243–255
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Abstract |
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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. |
Keywords
closed geodesics, surface of revolution
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Mathematical Subject Classification 2010
Primary: 53C20, 58E10
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Milestones
Received: 30 August 2015
Revised: 7 March 2016
Accepted: 25 March 2016
Published: 10 November 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Lee Kennard | |
| Department of Mathematics University of Oklahoma Norman, OK 73019 United States |
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| Jordan Rainone | |
| Department of Mathematics Stony Brook University 100 Nicolls Road Stony Brook, NY 11794 United States |
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