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

Lee Kennard, Jordan Rainone

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)243-255
Number of pages13
JournalInvolve
Volume10
Issue number2
DOIs
StatePublished - 2017

Keywords

  • closed geodesics
  • surface of revolution

ASJC Scopus subject areas

  • Mathematics(all)

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