# sphere theorem from global differential geometry

This theorem, as do Carmo refers it, is one of the most beautiful theorems in Riemannian geometry:

sphere theorem. Let $M$ be a n-dimensional compact simply connected Riemannian manifold^{}, whose sectional curvature^{} $K$ satisfies

$$ |

Then $M$ is homeomorphic to a sphere.

## References

- 1 M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.

Title | sphere theorem from global differential geometry |
---|---|

Canonical name | SphereTheoremFromGlobalDifferentialGeometry |

Date of creation | 2013-03-22 15:54:09 |

Last modified on | 2013-03-22 15:54:09 |

Owner | juanman (12619) |

Last modified by | juanman (12619) |

Numerical id | 8 |

Author | juanman (12619) |

Entry type | Theorem |

Classification | msc 53C21 |

Classification | msc 53C20 |

Related topic | Curvature^{} |

Related topic | Connection^{} |