{
  "id": "1711.11435",
  "version": "v1",
  "published": "2017-11-28T22:16:43.000Z",
  "updated": "2017-11-28T22:16:43.000Z",
  "title": "Virtual immersions, and a characterization of symmetric spaces",
  "authors": [
    "Ricardo A. E. Mendes",
    "Marco Radeschi"
  ],
  "comment": "11 pages. arXiv admin note: text overlap with arXiv:1708.05881",
  "categories": [
    "math.DG"
  ],
  "abstract": "We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold admits a virtual immersion with skew symmetric second fundamental form, if and only if it is a symmetric space, and in this case the virtual immersion is essentially unique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-28T22:16:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric space",
      "skew symmetric second fundamental form",
      "characterization",
      "virtual immersions possess",
      "pseudo-riemannian vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}