{
  "id": "0710.2911",
  "version": "v3",
  "published": "2007-10-15T20:59:48.000Z",
  "updated": "2010-06-28T19:34:33.000Z",
  "title": "Spectral isolation of bi-invariant metrics on compact Lie groups",
  "authors": [
    "Carolyn S. Gordon",
    "Dorothee Schueth",
    "Craig J. Sutton"
  ],
  "comment": "10 pages, new title, revised abstract and introduction, minor typos corrected, to appear in Ann. Inst. Fourier (Grenoble)",
  "journal": "Ann. Inst. Fourier 60 (2010), no. 5, 1617-1628",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that a bi-invariant metric on a compact connected Lie group $G$ is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric $g_0$ on $G$ there is a positive integer $N$ such that, within a neighborhood of $g_0$ in the class of left-invariant metrics of at most the same volume, $g_0$ is uniquely determined by the first $N$ distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where $G$ is simple, $N$ can be chosen to be two.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-06-28T19:34:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "58J50"
    ],
    "keywords": [
      "bi-invariant metric",
      "compact lie groups",
      "spectral isolation",
      "left-invariant metrics",
      "compact connected lie group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2911G"
    }
  }
}