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.
Funding Statement
The first author was partially supported by the Grant-in-Aid for Young Scientists No. 19K14527 and No. 23K12979. The second author was partially supported by the Grant-in-Aid for Young Scientists No. 19K14526 and (B) No. 20H01801. The third and fourth authors were partially supported by (B) No. 21H00981 and (B) No. 17H02839, respectively, from Japan Society for the Promotion of Science.
Citation
Shintaro AKAMINE. Atsufumi HONDA. Masaaki UMEHARA. Kotaro YAMADA. "Null hypersurfaces as wave fronts in Lorentz–Minkowski space." J. Math. Soc. Japan Advance Publication 1 - 30, November, 2024. https://doi.org/10.2969/jmsj/90929092
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