{
  "id": "math/0105119",
  "version": "v2",
  "published": "2001-05-15T17:30:08.000Z",
  "updated": "2002-02-10T20:14:50.000Z",
  "title": "New Cohomogeneity One Metrics With Spin(7) Holonomy",
  "authors": [
    "M. Cvetic",
    "G. W. Gibbons",
    "H. Lu",
    "C. N. Pope"
  ],
  "comment": "Latex, 15 pages. Improved and simplified construction of metrics",
  "journal": "J.Geom.Phys.49:350-365,2004",
  "doi": "10.1016/S0393-0440(03)00108-6",
  "categories": [
    "math.DG",
    "hep-th"
  ],
  "abstract": "We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A_8, is complete and non-singular on R^8. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S^4, and are denoted by B_8^+, B_8^- and B_8. The metrics on B_8^+ and B_8^- occur in families with a non-trivial parameter. The metric on B_8 arises for a limiting value of this parameter, and locally this metric is the same as the one for A_8. The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP^3. We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of opposite dualities) for the B_8 manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-02-10T20:14:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cohomogeneity",
      "explicit non-singular metrics",
      "non-compact riemannian",
      "holonomy spin",
      "complete metrics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 580616
    }
  }
}