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arXiv · 2003.12254

Hypersurfaces with Light-Like Points in a Lorentzian Manifold II

Masaaki Umehara·Kotaro Yamada
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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.

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Masaaki Umehara, Kotaro Yamada. 2020-03-27. Hypersurfaces with Light-Like Points in a Lorentzian Manifold II. https://arxiv.org/abs/2003.12254

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