{
  "id": "1010.3661",
  "version": "v1",
  "published": "2010-10-18T17:48:53.000Z",
  "updated": "2010-10-18T17:48:53.000Z",
  "title": "Homogeneous Einstein metrics on G_2/T",
  "authors": [
    "Andreas Arvanitoyeorgos",
    "Ioannis Chrysikos",
    "Yusuke Sakane"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M=G_2/T$. By computing a Gr\\\"obner basis for a system of polynomials of multi-variables we prove that this manifold admits exactly two non-K\\\"ahler invariant Einstein metrics. Thus $G_2/T$ turns out to be the first known example of an exceptional full flag manifold which admits at least one non-K\\\"ahler and not normal homogeneous Einstein metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-18T17:48:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional full flag manifold",
      "invariant riemannian metric",
      "normal homogeneous einstein metric",
      "invariant einstein metrics",
      "einstein equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3661A"
    }
  }
}