On the existence of infinitely many closed geodesics on orbifolds of revolution

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dc.creatorBorzellino, Joseph E.
dc.creatorJordan-Squire, Christopher R.
dc.creatorPetrics, Gregory C.
dc.creatorSullivan, D. Mark
dc.date2006-02-27
dc.date.accessioned2026-07-07T07:03:48Z
dc.date.available2026-07-07T07:03:48Z
dc.descriptionUsing 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 S^2 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.
dc.description21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.html
dc.identifierhttps://arxiv.org/abs/math/0602595
dc.identifierhttp://arxiv.org/abs/math/0602595
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109115
dc.subjectDifferential Geometry
dc.subject53C22; 58E10
dc.titleOn the existence of infinitely many closed geodesics on orbifolds of revolution
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