Manifolds without 1/k-geodesic

Details Manifolds without 1/k-geodesic Manifolds without 1/k-geodesic

2006-10-17

arxiv.org/abs/math/0610503v1

Mathematics

Differential Geometry

11 pages, 8 figures

Scientific paper

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.

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