English

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.

Keywords

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

R2 v1 2026-06-21T18:09:46.468Z