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March 2021 Hypersurfaces with light-like points in a Lorentzian manifold II
Masaaki Umehara, Kotaro Yamada
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Kodai Math. J. 44(1): 69-76 (March 2021). DOI: 10.2996/kmj44104

Abstract

In the authors' previous work, it was shown that if a zero mean curvature $C^4$-differentiable hypersurface in an arbitrarily given Lorentzian manifold admits a degenerate light-like point, then the hypersurface contains a light-like geodesic segment passing through the point. The purpose of this paper is to point out that the same conclusion holds with just $C^3$-differentiability of the hypersurfaces.

Funding Statement

The second author was partially supported by the Grant-in-Aid for Scientific Research (B) No. 17H02839 from Japan Society for the Promotion of Science.

Acknowledgment

The authors thank Professor Udo Hertrich-Jeromin for valuable comments.

Citation

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Masaaki Umehara. Kotaro Yamada. "Hypersurfaces with light-like points in a Lorentzian manifold II." Kodai Math. J. 44 (1) 69 - 76, March 2021. https://doi.org/10.2996/kmj44104

Information

Received: 30 March 2020; Revised: 9 July 2020; Published: March 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2996/kmj44104

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

Keywords: light-like geodesic , Lorentzian manifold , maximal hypersurface , zero mean curvature

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 1 • March 2021
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