Physical Mathematics

Induced Riemannian Structures and Topology of Null Hypersurfaces in Lorentzian Manifold

Abstract

Karimumuryango M

Given a null hypersurface of a Lorentzian manifold, we induce a Riemannian metric on the null hypersurface using a normalizing field defined on some open set containing the null hypersurface. We establish links between the null geometry and basics invariants of the associated Riemannian metric. This allowed us, using some comparison theorems from Riemannian geometry, to get important results on the topology of the null hypersurface.