Characterization of null cones under a Ricci curvature condition (Q2069932)

Null hypersurfaces arise in a natural way in Lorentzian geometry and they have no Riemannian counterpart. It is not easy to study them due to the fact that the induced metric is degenerate, so it is important to develop ideas and tools to get a best understanding on their geometry and topology. This paper is devoted to the study of the conditions under which a totally umbilic immersed null hypersurface in a Lorentzian manifold is contained in a null cone. The main tool used for this purpose is the rigging technique and the analysis of the Raychaudhuri equation for an immersed null hypersurface. Conditions to ensure that the null conjugate locus is a single point and the existence of two vertices in a null cone are also given.