{
  "id": "1706.09012",
  "version": "v1",
  "published": "2017-06-27T18:59:35.000Z",
  "updated": "2017-06-27T18:59:35.000Z",
  "title": "Spectral uniqueness of the bi-invariant metric on symplectic groups",
  "authors": [
    "Emilio A. Lauret"
  ],
  "categories": [
    "math.DG",
    "math.SP"
  ],
  "abstract": "In this short note, we prove that a bi-invariant Riemannian metric on $\\mathrm{Sp}(n)$ is uniquely determined by the spectrum of its Laplace operator within the class of left-invariant metrics on $\\mathrm{Sp}(n)$, for any $n\\geq5$ or $n=3$. In other words, on any of these compact simple Lie groups, every left-invariant metric which is not right-invariant cannot be isospectral to a bi-invariant metric. The proof uses a very strong spectral obstruction proved by Gordon, Schueth and Sutton.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-27T18:59:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J53",
      "53C30",
      "53C35"
    ],
    "keywords": [
      "bi-invariant metric",
      "spectral uniqueness",
      "symplectic groups",
      "compact simple lie groups",
      "left-invariant metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}