{
  "id": "0912.4207",
  "version": "v4",
  "published": "2009-12-21T16:45:03.000Z",
  "updated": "2011-10-19T12:35:36.000Z",
  "title": "Clifford structures on Riemannian manifolds",
  "authors": [
    "Andrei Moroianu",
    "Uwe Semmelmann"
  ],
  "comment": "Final version, 28 pages",
  "journal": "Adv. Math. 228, 940-967 (2011)",
  "doi": "10.1016/j.aim.2011.06.006",
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford structures: K\\\"ahler, quaternion-K\\\"ahler and Riemannian products of quaternion-K\\\"ahler manifolds, several classes of 8-dimensional manifolds, families of real, complex and quaternionic Grassmannians, as well as Rosenfeld's elliptic projective planes, which are symmetric spaces associated to the exceptional simple Lie groups. As an application, we classify all Riemannian manifolds whose metric is bundle-like along the curvature constancy distribution, generalizing well-known results in Sasakian and 3-Sasakian geometry.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-10-19T12:35:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C26",
      "53C35",
      "53C10",
      "53C15"
    ],
    "keywords": [
      "riemannian manifolds",
      "clifford structures",
      "exceptional simple lie groups",
      "rosenfelds elliptic projective planes",
      "curvature constancy distribution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4207M"
    }
  }
}