CONVEX REGIONS OF LORENTZIAN MANIFOLDS

In this paper we study the geodesic connectedness of some open connected subsets (regions) of a Lorentzian manifold, using a convexity property of the boundary of such regions. Necessary and sufficient conditions on the metric are given for the convexity of the boundary of such regions. Finally it is presented a result on the geodesic connectedeness of the whole manifold which relates the asymptotic behaviour of the coefficients of the metric to the convexity of the boundary of a family of regions which cover the manifold.