{
  "id": "1102.3347",
  "version": "v4",
  "published": "2011-02-16T14:31:19.000Z",
  "updated": "2012-12-11T09:39:45.000Z",
  "title": "Sobolev metrics on the manifold of all Riemannian metrics",
  "authors": [
    "Martin Bauer",
    "Philipp Harms",
    "Peter W. Michor"
  ],
  "comment": "20 pages, misprints corrected",
  "journal": "Journal of Differential Geometry 94, 2 (2013), 187-208",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "On the manifold $\\Met(M)$ of all Riemannian metrics on a compact manifold $M$ one can consider the natural $L^2$-metric as described first by \\cite{Ebin70}. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition when Ricci flow is a gradient flow for one of these metrics.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-12-11T09:39:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D17",
      "58E30",
      "35A01"
    ],
    "keywords": [
      "riemannian metrics",
      "sobolev metrics",
      "compact manifold",
      "higher order",
      "ricci flow"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3347B"
    }
  }
}