{
  "id": "math/0305140",
  "version": "v2",
  "published": "2003-05-09T14:08:47.000Z",
  "updated": "2010-05-06T12:45:51.000Z",
  "title": "Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length",
  "authors": [
    "Andrei Moroianu",
    "Liviu Ornea"
  ],
  "journal": "C. R. Math. Acad. Sci. Paris 338 (2004), 561-564",
  "doi": "10.1016/j.crma.2004.01.030",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that on a compact $n$-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue $\\lambda$ of the Dirac operator satisfies the inequality $\\lambda^2 \\geq \\frac{n-1}{4(n-2)}\\inf_M Scal$. In the limiting case the universal cover of the manifold is isometric to $R\\times N$ where $N$ is a manifold admitting Killing spinors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-06T12:45:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "58B40"
    ],
    "keywords": [
      "constant length",
      "eigenvalue estimates",
      "dirac operator satisfies",
      "non-trivial harmonic",
      "dimensional spin manifold admitting"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5140M"
    }
  }
}