A remark on the Morse Theorem about infinitely many geodesics between two points

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.

Contribution to the proceedings of the "International Meeting on Differential Geometry, Córdoba 2010". 7 pages, AMSLaTex. v2: minor revision, one reference and related comments added

References in corpus (2)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

Cited by in corpus (1)

• On the growth rate of geodesic chords