Preprint January 1, 2006.
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.
2006 JOSEPH E. BORZELLINO, CHRISTOPHER R. JORDAN-SQUIRE, GREGORY C. PETRICS, AND D. MARK SULLIVAN.
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