Abstract

We study 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. As an application, 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.

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