{
  "id": "math/0407121",
  "version": "v2",
  "published": "2004-07-08T08:32:22.000Z",
  "updated": "2004-07-15T13:05:06.000Z",
  "title": "Sphere Theorem for Manifolds with Positive Curvature",
  "authors": [
    "Bazanfare Mahaman"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we prove that, for any integer $n\\ge 2,$ there exists an $\\epsilon_{n} \\ge 0$ so that if $M$ is an n-dimensional complete manifold with sectional curvature $ K_{M}\\ge 1$ and if $M$ has conjugate radius bigger than $\\frac{\\pi}{2} $ and contains a geodesic loop of length $2(\\pi -\\epsilon_{n}),$ then $M$ is diffeomorphic to the Euclidian unit sphere $S^{n}.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-07-15T13:05:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21"
    ],
    "keywords": [
      "sphere theorem",
      "positive curvature",
      "euclidian unit sphere",
      "n-dimensional complete manifold",
      "conjugate radius bigger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7121M"
    }
  }
}