Manifolds without 1/k-geodesic

Publication date: 16 October 2006

Abstract: It is a question by C.Sormani that whether there exists a

k i n m a t h b b N

, such that any compact, smooth and simply connected manifold has a 1/k-geodesic. We prove in this paper that this is not true by showing for each

k

, there exists a metric on the sphere such that it has no 1/k-geodesic.

This page was built for publication: Manifolds without 1/k-geodesic