2006/02/27 by Joseph E. Borzellino, Christopher R. Jordan-Squire, Borzellino, Joseph E. +5 · 1 citation
Mathematics · #53C22 #58E10 #Differential Geometry (math.DG) #FOS: Mathematics #Geodesic #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #History #Mathematical analysis #Mathematics #Pure mathematics #math.DG #msc:53C22 #msc:58E10
paper · pdf · doi:10.48550/arxiv.math/0602595
published in arXiv (Cornell University) (Cornell University) · 21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.html
arxiv created 2006/02/27 · openalex publication_date 2006/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.