The convexity radius of a Riemannian manifold
Differential Geometry
2017-03-22 v3
Abstract
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Keywords
Cite
@article{arxiv.1412.0341,
title = {The convexity radius of a Riemannian manifold},
author = {James Dibble},
journal= {arXiv preprint arXiv:1412.0341},
year = {2017}
}
Comments
6 pages; corrected false statements in the first and third sections and an error in Lemma 2.4; removed one reference and added three others; made other minor stylistic edits