{
  "id": "1201.6455",
  "version": "v1",
  "published": "2012-01-31T06:38:20.000Z",
  "updated": "2012-01-31T06:38:20.000Z",
  "title": "Biharmonic submanifolds in a Riemannian manifold with non-positive curvature",
  "authors": [
    "Nobumitsu Nakauchi",
    "Hajime Urakawa"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that for an isometric immersion of a complete Riemannian manifold into a Riemannian manifold with non-positive curvature, the norm of the mean curvature vector field is square integrable, then it is minimal. This is a partial affirmative answer of the B. Y. Chen's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-31T06:38:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-positive curvature",
      "biharmonic submanifolds",
      "mean curvature vector field",
      "complete riemannian manifold",
      "chens conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.6455N"
    }
  }
}