{
  "id": "1305.7065",
  "version": "v3",
  "published": "2013-05-30T11:17:16.000Z",
  "updated": "2013-08-28T14:05:43.000Z",
  "title": "Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold",
  "authors": [
    "Shun Maeta"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider biharmonic maps $\\phi:(M,g)\\rightarrow (N,h)$ from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. Assume that $\\alpha$ satisfies $1<\\alpha<\\infty$. If for such an $\\alpha$, $\\int_M|\\tau(\\phi)|^{\\alpha}dv_g<\\infty$ and $\\int_M|d\\phi|^2dv_g<\\infty,$ where $\\tau(\\phi)$ is the tension field of $\\phi$, then we show that $\\phi$ is harmonic. For a biharmonic submanifold, we obtain that the above assumption $\\int_M|d\\phi|^2dv_g<\\infty$ is not necessary. These results give affirmative partial answers to the global version of generalized Chen's conjecture.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-08-28T14:05:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "53C43"
    ],
    "keywords": [
      "complete riemannian manifold",
      "biharmonic maps",
      "non-positively curved manifold",
      "non-positive sectional curvature",
      "biharmonic submanifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.7065M"
    }
  }
}