{
  "id": "2103.13849",
  "version": "v1",
  "published": "2021-03-25T13:59:34.000Z",
  "updated": "2021-03-25T13:59:34.000Z",
  "title": "Singularities of spacelike mean curvature one surfaces in de Sitter space",
  "authors": [
    "Atsufumi Honda",
    "Himemi Sato"
  ],
  "comment": "30 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we study the singularities of spacelike constant mean curvature one (CMC 1) surfaces in the de Sitter 3-space. We prove the duality between generalized conelike singular points and 5/2-cuspidal edges on spacelike CMC 1 surfaces. To describe the duality between $A_{k+3}$ singularities and cuspidal $S_k$ singularities, we introduce two invariants, called the $\\alpha$-invariant and $\\sigma$-invariant, of spacelike CMC 1 surfaces at their singular points. Moreover, we give a classification of non-degenerate singular points on spacelike CMC 1 surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T13:59:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "57R45",
      "53A35",
      "53C42",
      "53B30"
    ],
    "keywords": [
      "spacelike mean curvature",
      "sitter space",
      "singularities",
      "spacelike cmc",
      "spacelike constant mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}