{
  "id": "1208.0473",
  "version": "v2",
  "published": "2012-08-02T13:02:59.000Z",
  "updated": "2012-10-31T17:08:56.000Z",
  "title": "Biminimal properly immersed submanifolds in complete Riemannian manifolds of non-positive curvature",
  "authors": [
    "Shun Maeta"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider a non-negative biminimal properly immersed submanifold $M$ (that is, a biminimal properly immersed submanifold with $\\lambda\\geq0$) in a complete Riemannian manifold $N$ with non-positive sectional curvature. Assume that the sectional curvature $K^N$ of $N$ satisfies $K^N\\geq-L(1+{\\rm dist}_N(\\cdot, q_0)^2)^{\\frac{\\alpha}{2}}$ for some $L>0,$ $2>\\alpha \\geq 0$ and $q_0\\in N$. Then, we prove that $M$ is minimal. As a corollary, we give that any biharmonic properly immersed submanifold in a hyperbolic space is minimal. These results give affirmative partial answers to the global version of generalized Chen's conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-31T17:08:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "53C43"
    ],
    "keywords": [
      "complete riemannian manifold",
      "non-positive curvature",
      "sectional curvature",
      "hyperbolic space",
      "non-negative biminimal properly immersed submanifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.0473M"
    }
  }
}