{
  "id": "0907.0928",
  "version": "v2",
  "published": "2009-07-06T07:38:38.000Z",
  "updated": "2009-09-03T12:29:14.000Z",
  "title": "Wave equations and the LeBrun-Mason correspondence",
  "authors": [
    "Fuminori Nakata"
  ],
  "comment": "33 pages; section 3 revised",
  "categories": [
    "math.DG"
  ],
  "abstract": "The LeBrun-Mason twistor correspondences for $S^1$-invariant self-dual Zollfrei metrics are explicitly established. We give explicit formulas for the general solutions of the wave equation and the monopole equation on the de Sitter three-space under the assumption for the tameness at infinity by using Radon-type integral transforms, and the above twistor correspondence is described by using these formulas. We also obtain a critical condition for the LeBrun-Mason twistor spaces, and show that the twistor theory does not work well for twistor spaces which do not satisfy this condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-03T12:29:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C28",
      "35L05",
      "53C50",
      "32G10"
    ],
    "keywords": [
      "wave equation",
      "lebrun-mason correspondence",
      "invariant self-dual zollfrei metrics",
      "lebrun-mason twistor correspondences",
      "radon-type integral transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 825073,
      "adsabs": "2009arXiv0907.0928N"
    }
  }
}