{
  "id": "1910.10028",
  "version": "v1",
  "published": "2019-10-22T15:04:21.000Z",
  "updated": "2019-10-22T15:04:21.000Z",
  "title": "Symmetric affine surfaces with torsion",
  "authors": [
    "Daniela D'Ascanio",
    "Peter Gilkey",
    "Pablo Pisani"
  ],
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion is assumed parallel. This generalizes a previous result of Opozda in the torsion free setting; these geometries are all locally homogeneous. If the torsion is not parallel, we assume the underlying surface is locally homogeneous and provide a complete classification in this setting as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-22T15:04:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete classification",
      "study symmetric affine surfaces",
      "torsion free",
      "non-vanishing torsion tensor",
      "local geometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}