Null hypersurfaces as wave fronts in Lorentz-Minkowski space

2022/03/06 by Akamine, Shintaro, Honda, Atsufumi, Umehara, Masaaki +1 · 1 citation
#53B30 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C50 #Secondary 53C42

paper · doi:10.48550/arxiv.2203.02864

Abstract

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.

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• The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition

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