{
  "id": "0807.1808",
  "version": "v2",
  "published": "2008-07-11T09:45:14.000Z",
  "updated": "2008-10-16T11:12:15.000Z",
  "title": "Surfaces with Parallel Mean Curvature Vector in S^2xS^2 and H^2xH^2",
  "authors": [
    "Francisco Torralbo",
    "Francisco Urbano"
  ],
  "comment": "30 pages. Corrreted typos, added a theorem and a section",
  "categories": [
    "math.DG"
  ],
  "abstract": "Two holomorphic Hopf differentials for surfaces of non-null parallel mean curvature vector in S^2xS^2 and H^2xH^2 are constructed. A 1:1 correspondence between these surfaces and pairs of constant mean curvature surfaces of S^2xR and H^2xR is established. Using that, surfaces with vanishing Hopf differentials (in particular spheres with parallel mean curvature vector) are classified and a rigidity result for constant mean curvature surfaces of S^2xR and H^2xR is proved.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-16T11:12:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B25",
      "53C40"
    ],
    "keywords": [
      "constant mean curvature surfaces",
      "non-null parallel mean curvature vector",
      "holomorphic hopf differentials",
      "rigidity result",
      "vanishing hopf differentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1808T"
    }
  }
}