2 research outputs found
On the existence of infinitely many closed geodesics on orbifolds of revolution
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 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.Comment: 21 pages, 4 figures; for a PDF version see
http://www.calpoly.edu/~jborzell/Publications/publications.htm
Closed Geodesics on Orbifolds of Revolution
Using the theory of geodesics on surfaces of revolution, we show 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\u27s 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\u27s result does not hold in the wider class of closed surfaces with cone manifold structures