Null hypersurfaces as wave fronts in Lorentz-Minkowski space
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 $\boldsymbol{R}^{n+1}_1$ are canonically induced by hypersurfaces in the $n$-dimensional Euclidean space $\boldsymbol{R}^n_0$. 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 light-like complete null hypersurfaces whose singular sets are compact.