{
  "id": "1208.5510",
  "version": "v4",
  "published": "2012-08-27T21:18:46.000Z",
  "updated": "2014-06-10T17:19:51.000Z",
  "title": "Essential Killing fields of parabolic geometries",
  "authors": [
    "Andreas Čap",
    "Karin Melnick"
  ],
  "comment": "50 pages. Minor corrections, references updated",
  "journal": "Indiana Univ. Math. J. 62 No. 6 (2013), 1917-1953",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian, almost quaternionic, and contact parabolic geometries, including CR structures, to obtain descriptions of the possible dynamics of such flows near the fixed point and strong restrictions on the curvature. In some cases, we can show vanishing of the curvature on a nonempty open set. Deriving consequences for a specific geometry entails evaluating purely algebraic and representation-theoretic criteria in the model homogeneous space. Published in Indiana University Mathematics Journal.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-10T17:19:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic geometry",
      "essential killing fields",
      "indiana university mathematics journal",
      "geometry entails evaluating purely algebraic",
      "higher order fixed points"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.5510C"
    }
  }
}