Spaces of Geodesics

• Spaces of Geodesics in Aportaciones Matematicas, Serie: Notas de Investigacion No. 8, ed. L. Del Riego. San Luis Potosi: UASLP, 1993. pp.67--79

  This is a survey of the history and present knowledge of the space of geodesics of a manifold with a linear connection. It includes some new results and some new proofs of old results.

• Spaces of Geodesics: Products, Coverings, Connectedness (with J. Beem and R. Low), Geometriae Dedicata 59 (1996) 51--64

  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 $\R^n$.