Spaces of Geodesics: Products, Coverings, Connectedness
dg-ga
2016-08-31 v1 Differential Geometry
Abstract
We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient conditions for a space to be geodesically connected in terms of the topology of its space of geodesics. We find the space of geodesics of an -dimensional Hadamard manifold is the same as that of .
Cite
@article{arxiv.dg-ga/9501005,
title = {Spaces of Geodesics: Products, Coverings, Connectedness},
author = {J. K. Beem and R. J. Low and P. E. Parker},
journal= {arXiv preprint arXiv:dg-ga/9501005},
year = {2016}
}
Comments
17 pages, no figures, process with AMS-LaTeX 1.1, to appear in Geometriae Dedicata