{
  "id": "1501.00852",
  "version": "v1",
  "published": "2015-01-05T13:20:47.000Z",
  "updated": "2015-01-05T13:20:47.000Z",
  "title": "Explicit ambient metrics and holonomy",
  "authors": [
    "Ian M. Anderson",
    "Thomas Leistner",
    "Pawel Nurowski"
  ],
  "comment": "29 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic rank 2 and 3 distributions in respective dimensions 5 and 6. The corresponding explicit Fefferman-Graham ambient metrics provide a large class of metrics with holonomy equal to the exceptional non-compact Lie group $\\mathbf{G}_2$ as well as ambient metrics with holonomy contained in $\\mathbf{Spin}(4,3)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-05T13:20:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C29",
      "53A30",
      "53C50"
    ],
    "keywords": [
      "explicit ambient metrics",
      "conformal structures",
      "exceptional non-compact lie group",
      "corresponding explicit fefferman-graham ambient metrics",
      "generic rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150100852A"
    }
  }
}