{
  "id": "1712.07227",
  "version": "v1",
  "published": "2017-12-19T21:40:32.000Z",
  "updated": "2017-12-19T21:40:32.000Z",
  "title": "Ricci-flat metrics on the cone over $\\mathbb{CP}^2 \\# \\overline{\\mathbb{CP}^2}$",
  "authors": [
    "Dmitri Bykov"
  ],
  "comment": "56 pages, 4 figures",
  "categories": [
    "hep-th",
    "gr-qc",
    "math.DG"
  ],
  "abstract": "We describe a framework for constructing the Ricci-flat metrics on the total space of the canonical bundle over $\\mathbb{CP}^2 \\# \\overline{\\mathbb{CP}^2}$ (the del Pezzo surface of rank one). We construct explicitly the first-order deformation of the so-called `orthotoric metric' on this manifold. We also show that the deformation of the corresponding conformal Killing-Yano form does not exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T21:40:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci-flat metrics",
      "corresponding conformal killing-yano form",
      "del pezzo surface",
      "total space",
      "orthotoric metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}