Null hypersurfaces as wave fronts in Lorentz–Minkowski space

In this paper, we show that “$L$-complete null hypersurfaces” (i.e. ruled null hypersurfaces foliated by entirety of light-like lines) as wave fronts in $(n+1)$-dimensional Lorentz–Minkowski space are canonically induced by hypersurfaces in $n$-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.