  In this paper, we show that ``$L$-complete null hypersurfaces'' (i.e. ruled
hypersurfaces foliated by entirety of light-like lines) as wave fronts in the
$(n+1)$-dimensional Lorentz-Minkowski space are canonically induced by
hypersurfaces in the $n$-dimensional Euclidean space. As an application, we
show that most of null wave fronts can be realized as restrictions of certain
$L$-complete null wave fronts. Moreover, we determine $L$-complete null wave
fronts whose singular sets are compact.
