{
  "id": "math/0406426",
  "version": "v1",
  "published": "2004-06-22T10:16:27.000Z",
  "updated": "2004-06-22T10:16:27.000Z",
  "title": "Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces",
  "authors": [
    "Benoit Daniel"
  ],
  "comment": "27 pages, 1 figure",
  "journal": "Trans. Amer. Math. Soc. 361 (2009), no. 12, 6255-6282",
  "categories": [
    "math.DG"
  ],
  "abstract": "We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in S^n x R or H^n x R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S^2 x R or H^2 x R, obtained by rotating the shape operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-22T10:16:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42",
      "53A35",
      "53B25"
    ],
    "keywords": [
      "minimal surface",
      "isometric immersions",
      "applications",
      "n-dimensional riemannian manifold",
      "second fundamental forms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6426D"
    }
  }
}