Closed geodesics with local homology in maximal degree on non-compact manifolds
Differential Geometry
2017-12-27 v2 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1707.00257,
title = {Closed geodesics with local homology in maximal degree on non-compact manifolds},
author = {Luca Asselle and Marco Mazzucchelli},
journal= {arXiv preprint arXiv:1707.00257},
year = {2017}
}
Comments
36 pages, 3 figures. Version 2: minor modifications. To appear in Differential Geometry and its Applications