On the growth rate of geodesic chords

Abstract

We show that every forward complete Finsler manifold of infinite fundamental group and not homotopy-equivalent to $S^1$ has infinitely many geometrically distinct geodesics joining any given pair of points $p$ and $q$. In the special case in which ${\beta }_1(M;\mathbb{Z})\ge 1$ and $M$ is closed, the number of geometrically distinct geodesics between two points grows at least logarithmically.

10 pages, to appear in Differential Geometry and its Applications

References in corpus (2)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• A remark on the Morse Theorem about infinitely many geodesics between two points