A remark on the Morse Theorem about infinitely many geodesics between two points
Differential Geometry
2011-12-30 v2
Abstract
We show that any two non-conjugate points on a forward or backward complete connected Finsler manifold can be joined by infinitely many geodesics which are not covered by finitely many closed ones, provided that the Betti numbers of the based loop space grow unbounded.
Cite
@article{arxiv.1105.3923,
title = {A remark on the Morse Theorem about infinitely many geodesics between two points},
author = {Erasmo Caponio and Miguel Angel Javaloyes},
journal= {arXiv preprint arXiv:1105.3923},
year = {2011}
}
Comments
Contribution to the proceedings of the "International Meeting on Differential Geometry, C\'ordoba 2010". 7 pages, AMSLaTex. v2: minor revision, one reference and related comments added