2016/03/28 by Christian Lange, Lange, Christian
Mathematics · #53C22 #55R55 #57R18 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53C22 #msc:55R55 #msc:57R18
paper · pdf · doi:10.48550/arxiv.1603.08455
27 pages, improved exposition, more details, minor inaccuracies fixed
arxiv created 2017/11/01 · arxiv updated 2017/11/02
We show that the geodesic period spectrum of a Riemannian 2-orbifold all of whose geodesics are closed depends, up to a constant, only on its orbifold topology and compute it. In the manifold case we recover the fact proved by Gromoll, Grove and Pries that all prime geodesics have the same length. In the appendix we partly strengthen our result in terms of conjugacy of contact forms and explain how to deduce rigidity on the real projective plane based on a systolic inequality due to Pu. (We do not use a Lusternik-Schnirelmann type theorem on the existence of at least three simple closed geodesics.)