Spaces of Geodesics: Products, Coverings, Connectedness

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 $n$-dimensional Hadamard manifold is the same as that of ${\mathbb{R}}^n$.

17 pages, no figures, process with AMS-LaTeX 1.1, to appear in Geometriae Dedicata