{
  "id": "math/0611371",
  "version": "v1",
  "published": "2006-11-13T07:58:09.000Z",
  "updated": "2006-11-13T07:58:09.000Z",
  "title": "Riemannian curvature: variations on different notions of positivity",
  "authors": [
    "Mohammed Larbi Labbi"
  ],
  "comment": "In french, extracted from habilitation thesis at Montpellier II University (France), 50 pages",
  "journal": "Habilitation thesis, July 2006, Montpellier II University, France",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study different notions of Riemannian curvatures: The $p$-curvatures which interpolate between the scalar curvature and the sectional curvature, the Gauss-Bonnet-Weyl curvatures form another interpolation from the scalar curvature to the Gauss-Bonnet integrand. We bring out the $(p,q)$-curvatures, which incorporate all the previous curvatures. We then examine the curvature term which appears in the classical Weitzenb\\\"ock formula. We also study the positivity properties of the $p$-curvatures, the second Gauss-Bonnet-Weyl curvature, the Einstein curvature and the isotropic curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-13T07:58:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C25",
      "53B20",
      "58A14",
      "58D17",
      "58E11"
    ],
    "keywords": [
      "riemannian curvature",
      "variations",
      "scalar curvature",
      "gauss-bonnet-weyl curvatures form",
      "second gauss-bonnet-weyl curvature"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11371L"
    }
  }
}