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