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