{
  "id": "2007.10006",
  "version": "v1",
  "published": "2020-07-20T11:23:49.000Z",
  "updated": "2020-07-20T11:23:49.000Z",
  "title": "On rotational surfaces in 3 dimensional de Sitter space with Weingarten condition",
  "authors": [
    "Burcu Bektaş Demirci"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this article, we study spacelike and timelike rotational surfaces in a 3--dimensional de Sitter space $\\mathbb{S}^3_1$ which are the orbit of a regular curve under the action of the orthogonal transformation of 4--dimensional Minkowski space $\\mathbb{E}^4_1$ leaving a spacelike, a timelike or a degenerate plane pointwise fixed. We determine the profile curve of such Weingarten rotational surfaces parameterized by the principal curvature. Then, we classify spacelike and timelike Weingarten rotational surface in $\\mathbb{S}^3_1$ with the principal curvatures $\\kappa$ and $\\lambda$ satisfying $\\kappa=a\\lambda+b$ or $\\kappa=a\\lambda^m$ for special cases of constants $a, b$ and $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T11:23:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C40",
      "53C42"
    ],
    "keywords": [
      "sitter space",
      "weingarten condition",
      "dimensional",
      "principal curvature",
      "timelike weingarten rotational surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}