Geodesic Connectedness of Affine Manifolds

Abstract

We discuss new sufficient conditions under which an affine manifold $(M,\nabla )$ is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexander and Karr, with the added advantage that they yield an elementary proof of the main result.

13 pages; minor changes in the introduction and section 3