  Rigging technique introduced in \cite{bi0} is a convenient way to address the
study of null hypersurfaces. It offers in addition the extra benefit of
inducing a Riemannian structure on the null hypersurface which is used to study
geometric and topological properties on it. In this paper we develop this
technique showing new properties and applications. We first discuss the very
existence of the rigging fields under prescribed geometric and topological
constraints. We consider the completeness of the induced rigged Riemannian
structure. This is potentially important because it allows to use most of the
usual Riemannian techniques.
