{
  "id": "math/0606299",
  "version": "v2",
  "published": "2006-06-13T09:30:49.000Z",
  "updated": "2010-03-24T14:30:42.000Z",
  "title": "The Gauss map of minimal surfaces in the Heisenberg group",
  "authors": [
    "Benoît Daniel"
  ],
  "comment": "17 pages, redaction improved.",
  "journal": "Int. Math. Res. Not. IMRN 2011 (2011), no. 3, 674-695",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the Gauss map of minimal surfaces in the Heisenberg group $\\mathrm{Nil}_3$ endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane $\\mathbb{H}^2$. Conversely, any nowhere antiholomorphic harmonic map into $\\mathbb{H}^2$ is the Gauss map of a nowhere vertical minimal surface. Finally, we study the image of the Gauss map of complete nowhere vertical minimal surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-24T14:30:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42",
      "53A35",
      "53C43"
    ],
    "keywords": [
      "gauss map",
      "heisenberg group",
      "vertical minimal surface",
      "left-invariant riemannian metric",
      "antiholomorphic harmonic map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6299D"
    }
  }
}