{
  "id": "0803.3885",
  "version": "v1",
  "published": "2008-03-27T10:46:34.000Z",
  "updated": "2008-03-27T10:46:34.000Z",
  "title": "Integral geometry under $G_2$ and $Spin(7)$",
  "authors": [
    "Andreas Bernig"
  ],
  "comment": "13 pages",
  "journal": "Israel J. Math. 184 (2011), 301-316",
  "categories": [
    "math.DG"
  ],
  "abstract": "A Hadwiger-type theorem for the exceptional Lie groups $G_2$ and $Spin(7)$ is proved. The algebras of $G_2$ or $Spin(7)$ invariant, translation invariant continuous valuations are both of dimension 10. Geometrically meaningful bases are constructed and the algebra structures are computed. Finally, the kinematic formulas for these groups are determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-27T10:46:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C65",
      "52A22"
    ],
    "keywords": [
      "integral geometry",
      "exceptional lie groups",
      "translation invariant continuous valuations",
      "hadwiger-type theorem",
      "kinematic formulas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3885B"
    }
  }
}