Null hypersurfaces as wave fronts in Lorentz-Minkowski space

Shintaro Akamine; Atsufumi Honda; Masaaki Umehara; Kotaro Yamada

Null hypersurfaces as wave fronts in Lorentz-Minkowski space

Differential Geometry 2024-06-11 v3

Authors: Shintaro Akamine , Atsufumi Honda , Masaaki Umehara , Kotaro Yamada

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.

Keywords

hypersurfaces lorentzian geometry

Cite

@article{arxiv.2203.02864,
  title  = {Null hypersurfaces as wave fronts in Lorentz-Minkowski space},
  author = {Shintaro Akamine and Atsufumi Honda and Masaaki Umehara and Kotaro Yamada},
  journal= {arXiv preprint arXiv:2203.02864},
  year   = {2024}
}

Comments

26 pages, 5 figures

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