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November 2019 Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space
Shintaro Akamine, Masaaki Umehara, Kotaro Yamada
Proc. Japan Acad. Ser. A Math. Sci. 95(9): 97-102 (November 2019). DOI: 10.3792/pjaa.95.97

Abstract

Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\mathbf{R}^{3}_{1}$. A complete light-like line in $\mathbf{R}^{3}_{1}$ is called an \textit{entire null line} on the surface $S$ in $\mathbf{R}^{3}_{1}$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $\mathbf{R}^{2}$, then it must be contained in a light-like plane (cf. Remark~3.3). Our example is critical in the sense that it is defined on a certain non-convex domain.

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Shintaro Akamine. Masaaki Umehara. Kotaro Yamada. "Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space." Proc. Japan Acad. Ser. A Math. Sci. 95 (9) 97 - 102, November 2019. https://doi.org/10.3792/pjaa.95.97

Information

Published: November 2019
First available in Project Euclid: 1 November 2019

zbMATH: 07213567
MathSciNet: MR4026357
Digital Object Identifier: 10.3792/pjaa.95.97

Subjects:
Primary: 53A10, 53B30
Secondary: 35M10

Rights: Copyright © 2019 The Japan Academy

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Vol.95 • No. 9 • November 2019
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