{
  "id": "math/0104256",
  "version": "v3",
  "published": "2001-04-26T22:46:50.000Z",
  "updated": "2002-04-29T11:31:51.000Z",
  "title": "Obstructions to positive curvature and symmetry",
  "authors": [
    "Anand Dessai"
  ],
  "comment": "21 pages, revised version, new title",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that the indices of certain twisted Dirac operators vanish on a $Spin$-manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\\geq 2$ or if the symmetry rank is one and $M$ is two connected. We also give examples of simply connected manifolds of positive Ricci curvature which do not admit a metric of positive sectional curvature and positive symmetry rank.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-04-29T11:31:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "57R20",
      "53C21",
      "19L47",
      "53C27"
    ],
    "keywords": [
      "positive curvature",
      "positive sectional curvature",
      "obstructions",
      "positive ricci curvature",
      "positive symmetry rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4256D"
    }
  }
}