{
  "id": "1006.1261",
  "version": "v2",
  "published": "2010-06-07T14:17:44.000Z",
  "updated": "2010-07-08T14:47:32.000Z",
  "title": "Totally umbilical hypersurfaces of manifolds admitting a unit Killing field",
  "authors": [
    "Rabah Souam",
    "Joeri Van der Veken"
  ],
  "comment": "minor corrections to v1",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that a Riemannian product of type M x R (where R denotes the Euclidean line) admits totally umbilical hypersurfaces if and only if M has locally the structure of a warped product and we give a complete description of the totally umbilical hypersurfaces in this case. Moreover, we give a necessary and sufficient condition under which a Riemannian three-manifold carrying a unit Killing field admits totally geodesic surfaces and we study local and global properties of three-manifolds satisfying this condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-08T14:47:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally umbilical hypersurfaces",
      "unit killing field",
      "manifolds admitting",
      "killing field admits",
      "field admits totally geodesic surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1261S"
    }
  }
}