{
  "id": "1311.1579",
  "version": "v1",
  "published": "2013-11-07T05:25:18.000Z",
  "updated": "2013-11-07T05:25:18.000Z",
  "title": "New homogeneous Einstein metrics on Stiefel manifolds",
  "authors": [
    "Andreas Arvanitoyeorgos",
    "Yusuke Sakane",
    "Marina Statha"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider invariant Einstein metrics on the Stiefel manifold $V_q\\bb{R} ^n$ of all orthonormal $q$-frames in $\\bb{R}^n$. This manifold is diffeomorphic to the homogeneous space $\\SO(n)/\\SO(n-q)$ and its isotropy representation contains equivalent summands. %This causes difficulty in the description of all $\\SO(n)$-invariant metrics. We prove, by assuming additional symmetries, that $V_4\\bb{R}^n$ $(n\\ge 6)$ admits at least four $\\SO(n)$-invariant Einstein metrics, two of which are Jensen's metrics and the other two are new metrics. Moreover, we prove that $V_5\\bb{R}^7$ admits at least six invariant Einstein metrics, two of which are Jensen's metrics and the other four are new metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-07T05:25:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C30",
      "13P10",
      "65H10",
      "68W30"
    ],
    "keywords": [
      "homogeneous einstein metrics",
      "stiefel manifold",
      "invariant einstein metrics",
      "isotropy representation contains equivalent summands",
      "jensens metrics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.difgeo.2014.01.007"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1263825,
      "adsabs": "2013arXiv1311.1579A"
    }
  }
}