{
  "id": "2212.13811",
  "version": "v1",
  "published": "2022-12-28T13:08:37.000Z",
  "updated": "2022-12-28T13:08:37.000Z",
  "title": "Intrinsic torsion and scalar curvature of Spin(7)-structure",
  "authors": [
    "Kamil Niedzialomski"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We obtain explicit formula for the intrinsic torsion of a ${\\rm Spin}(7)$-structure on an $8$--dimensional Riemannian manifold. The formula relates the intrinsic torsion with the Lee form $\\theta$ and $\\Lambda^3_{48}$--component $(\\delta\\Phi)_{48}$ of codifferential $\\delta\\Phi$ of the $4$--form defining given structure. Moreover, using the divergence formula obtained by the author for general Riemannian $G$--structure, we derive the formula for the scalar curvature in terms of norms of $\\theta$, $(\\delta\\Phi)_{48}$ and the divergence ${\\rm div}\\theta$. We justify the formula on appropriate examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-28T13:08:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intrinsic torsion",
      "scalar curvature",
      "dimensional riemannian manifold",
      "appropriate examples",
      "general riemannian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}