{
  "id": "1809.03639",
  "version": "v1",
  "published": "2018-09-10T23:59:08.000Z",
  "updated": "2018-09-10T23:59:08.000Z",
  "title": "On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space",
  "authors": [
    "A. Borisenko",
    "Y. Nikolayevsky"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider Finsler submanifolds $M^n$ of nonnegative Ricci curvature in a Minkowski space $\\mathbb{M}^{n+p}$ which contain a line or whose relative nullity index is positive. For hypersurfaces, submanifolds of codimension two or of dimension two, we prove that the submanifold is a cylinder, under a certain condition on the inertia of the pencil of the second fundamental forms. We give an example of a surface of positive flag curvature in a three-dimensional Minkowski space which is not locally convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T23:59:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C40",
      "53C60",
      "53C21"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "cylindricity",
      "second fundamental forms",
      "three-dimensional minkowski space",
      "finsler submanifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}