Induced Riemannian structures on null hypersurfaces

Given a null hypersurface L of a Lorentzian manifold, we construct a Riemannian metric on it from a fixed transverse vector field ζ. We study the relationship between the ambient Lorentzian manifold, the Riemannian manifold and the vector field ζ. As an application, we prove some new results on null hypersurfaces, as well as known ones, using Riemannian techniques.