Closed geodesics on compact orbifolds and on noncompact manifolds
arXiv:1909.10388
Abstract
We prove the existence of a nonconstant closed geodesic on every odd-dimensional compact Riemannian orbifold and on every connected, noncontractible Riemannian manifold that admits a cocompact, isometric group action. We deduce new restrictions on a compact Riemannian orbifold without such a geodesic; in particular, its orbifold fundamental group is a rational Poincaré duality group.
9 pages. Rational Poincaré duality property of orbifold fundamental groups added; further context and expanded proofs