{
  "id": "math/0309328",
  "version": "v2",
  "published": "2003-09-19T18:19:19.000Z",
  "updated": "2003-09-26T16:04:34.000Z",
  "title": "The smoothness of Riemannian submersions with nonnegative sectional curvature",
  "authors": [
    "Jianguo Cao",
    "Mei-Chi Shaw"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M^n$ be a complete, non-compact and $C^\\infty$-smooth Riemannian manifold with nonnegative sectional curvature. Suppose $\\Cal S$ is a soul of $M^n$. Then any distance non-increasing retraction $\\Psi: M^n \\to \\Cal S$ must give rise to a $C^\\infty$-smooth Riemannian submersion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-09-26T16:04:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C10"
    ],
    "keywords": [
      "nonnegative sectional curvature",
      "smoothness",
      "smooth riemannian manifold",
      "smooth riemannian submersion",
      "distance non-increasing retraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9328C"
    }
  }
}