Null hypersurfaces as wave fronts in Lorentz–Minkowski space

Abstract

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.