{
  "id": "1511.02568",
  "version": "v1",
  "published": "2015-11-09T05:06:55.000Z",
  "updated": "2015-11-09T05:06:55.000Z",
  "title": "A rigidity theorem of $ξ$-submanifolds in $\\mathbb{C}^{2}$",
  "authors": [
    "Xingxiao Li",
    "Xiufen Chang"
  ],
  "comment": "Submitted",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we first introduce the concept of $\\xi $-submanifold which is a natural generalization of self-shrinkers for the mean curvature flow and also an extension of $\\lambda$-hypersurfaces to the higher codimension. Then, as the main result, we prove a rigidity theorem for Lagrangian $\\xi $-submanifold in the complex $2$-plane $\\bbc^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-09T05:06:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A30",
      "53B25"
    ],
    "keywords": [
      "rigidity theorem",
      "submanifold",
      "mean curvature flow",
      "natural generalization",
      "higher codimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}