{
  "id": "1606.07595",
  "version": "v1",
  "published": "2016-06-24T08:13:02.000Z",
  "updated": "2016-06-24T08:13:02.000Z",
  "title": "On hypersurfaces of $\\mathbb{S}^2\\times\\mathbb{S}^2$",
  "authors": [
    "Francisco Urbano"
  ],
  "comment": "32 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We classify the homogeneous and isoparametric hypersurfaces of $\\mathbb{S}^2\\times\\mathbb{S}^2$. In the classification, besides the hypersurfaces $\\mathbb{S}^1(r)\\times\\mathbb{S}^2,\\,r\\in (0,1]$, it appears a family of hypersurfaces with three different constant principal curvatures and zero Gauss-Kronecker curvature. Also we classify the hypersurfaces of $\\mathbb{S}^2\\times\\mathbb{S}^2$ with at most two constant principal curvatures and, under certain conditions, with three constant principal curvatures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-24T08:13:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant principal curvatures",
      "zero gauss-kronecker curvature",
      "isoparametric hypersurfaces",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}