Manifolds without 1/k-geodesic
Abstract
Description
It is a question by C.Sormani that whether there exists a $k \in \mathbb N$, 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.
11 pages, 8 figures
11 pages, 8 figures