{
  "id": "1812.08676",
  "version": "v1",
  "published": "2018-12-20T16:25:24.000Z",
  "updated": "2018-12-20T16:25:24.000Z",
  "title": "Rotational Surfaces with second fundamental form of constant length",
  "authors": [
    "Alexandre P. Barreto",
    "Francisco Fontenele",
    "Luiz Hartmann"
  ],
  "categories": [
    "math.DG",
    "math.CA"
  ],
  "abstract": "We obtain an infinite family of complete non embedded rotational surfaces in $\\mathbb R^3$ whose second fundamental forms have length equal to one at any point. Also we prove that a complete rotational surface with second fundamental form of constant length is either a round sphere, a circular cylinder or, up to a homothety and a rigid motion, a member of that family. In particular, the round sphere and the circular cylinder are the only complete embedded rotational surfaces in $\\mathbb R^3$ with second fundamental form of constant length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-20T16:25:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A05",
      "53C42",
      "53C40",
      "14Q10"
    ],
    "keywords": [
      "second fundamental form",
      "constant length",
      "round sphere",
      "complete non embedded rotational surfaces",
      "circular cylinder"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}