{
  "id": "1810.00655",
  "version": "v1",
  "published": "2018-10-01T12:29:36.000Z",
  "updated": "2018-10-01T12:29:36.000Z",
  "title": "New homogeneous Einstein metrics on quaternionic Stiefel manifolds",
  "authors": [
    "Andreas Arvanitoyeorgos",
    "Yusuke Sakane",
    "Marina Statha"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider invariant Einstein metrics on the quaternionic Stiefel manifolds $V_p\\bb{H} ^n$ of all orthonormal $p$-frames in $\\bb{H}^n$. This manifold is diffeomorphic to the homogeneous space $\\Sp(n)/\\Sp(n-p)$ and its isotropy representation contains equivalent summands. We obtain new Einstein metrics on $V_{p}\\bb{H}^{n} \\cong \\Sp(n)/\\Sp(n-p)$, where $n = k_1 + k_2 + k_3$ and $p = n-k_3$. We view $V_{p}\\bb{H}^{n}$ as a total space over the genaralized Wallach space $\\Sp(n)/(\\Sp(k_1)\\times\\Sp(k_2)\\times\\Sp(k_3))$ and over the generalized flag manifold $\\Sp(n)/(\\U(p)\\times\\Sp(n-p))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T12:29:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C30",
      "13P10",
      "65H10",
      "68W30"
    ],
    "keywords": [
      "quaternionic stiefel manifolds",
      "homogeneous einstein metrics",
      "isotropy representation contains equivalent summands",
      "invariant einstein metrics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}