English

Manifolds without 1/k-geodesic

Differential Geometry 2007-05-23 v1

Abstract

It is a question by C.Sormani that whether there exists a kNk \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 kk, there exists a metric on the sphere such that it has no 1/k-geodesic.

Keywords

Cite

@article{arxiv.math/0610503,
  title  = {Manifolds without 1/k-geodesic},
  author = {Wing Kai Ho},
  journal= {arXiv preprint arXiv:math/0610503},
  year   = {2007}
}

Comments

11 pages, 8 figures