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

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

2011-05-19

arxiv.org/abs/1105.3923v2

Mathematics

Differential Geometry

Contribution to the proceedings of the "International Meeting on Differential Geometry, C\'ordoba 2010". 7 pages, AMSLaTex. v2

Scientific paper

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.

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