Work

Null hypersurfaces as wave fronts in Lorentz–Minkowski space

Year: 2024

Type: article

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.

Source: Journal of the Mathematical Society of Japan

DOI: 10.2969/jmsj/90929092

Authors: Shintaro AKAMINE, Atsufumi HONDA, Masaaki UMEHARA, Kotaro YAMADA

Institutions: Nihon University, Yokohama National University, Institute of Science Tokyo

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Differential geometrey of singularities and its applications, Analogues of the Weierstrass representation formula and extension problem of submanifolds at their singularities, Geometric invariants of singular points with applications to high dimensional wave fronts and mixed type hypersurfaces, 調和関数論を用いた平均曲率零曲面および関連する曲面論の研究