{
  "id": "1312.2554",
  "version": "v3",
  "published": "2013-12-09T19:33:13.000Z",
  "updated": "2015-03-12T21:31:59.000Z",
  "title": "Gaussian curvature in codimension > 1",
  "authors": [
    "Daniel Alvarez-Gavela"
  ],
  "comment": "Paper has been withdrawn because some of the claims made were false",
  "categories": [
    "math.DG"
  ],
  "abstract": "The Gaussian curvature $K$ is a fundamental geometric quantity discovered by Gauss in the case of surfaces embedded in $\\mathbb{R}^3$. One can naturally extend the definition of the Gaussian curvature to arbitrary submanifolds of $\\mathbb{R}^k$ so that the extrinsic interpretation of $K$, the Theorema Egregium and the Gauss-Bonnet Theorem still hold. We give a concise exposition of these classical facts.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-07T18:51:36.000Z",
      "comment": "6 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-12T21:31:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian curvature",
      "codimension",
      "fundamental geometric quantity",
      "arbitrary submanifolds",
      "gauss-bonnet theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2554A"
    }
  }
}