{
  "id": "1405.4230",
  "version": "v1",
  "published": "2014-05-16T16:21:41.000Z",
  "updated": "2014-05-16T16:21:41.000Z",
  "title": "Self-Shrinkers With Second Fundamental Form of Constant Length",
  "authors": [
    "Qiang Guang"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this note, we give a new and simple proof of a result in {\\cite{DX1}} which states that any smooth complete self-shrinker in $\\mathbb{R}^3$ with second fundamental form of constant length must be a generalized cylinder $\\mathbb{S}^k \\times \\mathbb{R}^{2-k}$ for some $k\\leq2$. Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-16T16:21:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second fundamental form",
      "constant length",
      "smooth complete self-shrinker",
      "smooth self-shrinkers",
      "gap theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4230G"
    }
  }
}