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Unpublished Paper
On the existence of infinitely many closed geodesics on orbifolds of revolution
Mathematics
  • Joseph Borzellino, California Polytechnic State University, San Luis Obispo
  • Christopher R. Jordan-Squire, Swarthmore College
  • Gregory C. Petrics, Middlebury College
  • D. Mark Sullivan, California Institute of Technology
Publication Date
1-1-2006
Abstract

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert’s theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert’s result does not hold in the wider class of closed surfaces with cone manifold structures.

Disciplines
Number of Pages
21
Publisher statement
Unpublished expository research article, published on preprint server www.arxiv.org at arXiv:math/0602595.
Citation Information
Joseph Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics and D. Mark Sullivan. "On the existence of infinitely many closed geodesics on orbifolds of revolution" (2006)
Available at: http://works.bepress.com/jborzell/10/