Mathematics – Differential Geometry
Scientific paper
2006-02-27
Mathematics
Differential Geometry
21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.html
Scientific paper
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.
Borzellino Joseph E.
Jordan-Squire Christopher R.
Petrics Gregory C.
Sullivan Mark D.
No associations
LandOfFree
On the existence of infinitely many closed geodesics on orbifolds of revolution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the existence of infinitely many closed geodesics on orbifolds of revolution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the existence of infinitely many closed geodesics on orbifolds of revolution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-485819