Closed geodesics with local homology in maximal degree on non-compact manifolds
arXiv:1707.00257 · doi:10.1016/j.difgeo.2017.11.007
Abstract
We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth under iteration forces the existence of infinitely many closed geodesics. For closed manifolds, this was a theorem due to Hingston.
36 pages, 3 figures. Version 2: minor modifications. To appear in Differential Geometry and its Applications