{
  "id": "math/0507075",
  "version": "v1",
  "published": "2005-07-04T17:38:20.000Z",
  "updated": "2005-07-04T17:38:20.000Z",
  "title": "Natural connections on the bundle of Riemannian metrics",
  "authors": [
    "Roberto Ferreiro Perez",
    "Jaime Muñoz Masque"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $FM,\\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\\mathrm{Diff}M$-invariant connection form on $J^1\\mathcal{M}_M\\times_MFM\\to J^1\\mathcal{M}_M$, which is Riemannian with respect to the universal metric on $J^1\\mathcal{M}_M\\times_MTM$, is proved. Aplications to the construction of universal Pontryagin and Euler forms, are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-04T17:38:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A55",
      "53B05",
      "53B21",
      "57R20",
      "58A20",
      "58D19"
    ],
    "keywords": [
      "riemannian metrics",
      "natural connections",
      "invariant connection form",
      "euler forms",
      "linear frames"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7075F"
    }
  }
}