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arXiv · 2203.02864

Null hypersurfaces as wave fronts in Lorentz-Minkowski space

Shintaro Akamine·Atsufumi Honda·Masaaki Umehara·Kotaro Yamada
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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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Shintaro Akamine, Atsufumi Honda, Masaaki Umehara, Kotaro Yamada. 2022-03-06. Null hypersurfaces as wave fronts in Lorentz-Minkowski space. https://arxiv.org/abs/2203.02864

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