{
  "id": "math/0509146",
  "version": "v1",
  "published": "2005-09-07T08:46:35.000Z",
  "updated": "2005-09-07T08:46:35.000Z",
  "title": "Nearly Kaehler and nearly parallel G_2-structures on spheres",
  "authors": [
    "Thomas Friedrich"
  ],
  "comment": "2 pages, Latex2e",
  "categories": [
    "math.DG"
  ],
  "abstract": "In some other context, the question was raised how many nearly K\\\"ahler structures exist on the sphere $\\S^6$ equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue $\\lambda = 12$ of the Laplacian acting on 2-forms. A similar result concerning nearly parallel $\\G_2$-structures on the round sphere $\\S^7$ holds, too. An alternative proof by Riemannian Killing spinors is also indicated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-07T08:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "81T30"
    ],
    "keywords": [
      "standard riemannian metric",
      "riemannian killing spinors",
      "structures",
      "short note",
      "round sphere"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9146F"
    }
  }
}