{
  "id": "2003.12254",
  "version": "v1",
  "published": "2020-03-27T06:52:14.000Z",
  "updated": "2020-03-27T06:52:14.000Z",
  "title": "Hypersurfaces with Light-Like Points in a Lorentzian Manifold II",
  "authors": [
    "Masaaki Umehara",
    "Kotaro Yamada"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-27T06:52:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53B30",
      "35M10"
    ],
    "keywords": [
      "zero mean curvature",
      "lorentzian manifold admits",
      "hypersurface contains",
      "conclusion holds",
      "light-like geodesic segment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}