# Gauss-Bonnet theorem for surfaces without boundary

If $S$ is a compact, orientable surface without boundary, then

$${\int}_{S}K=2\pi \chi (S),$$ |

where $K$ is the Gaussian curvature^{} of $S$ and $\chi (S)$ its
Euler-Poincaré characteristic. (http://planetmath.org/EulerrCharacteristic)

Title | Gauss-Bonnet theorem for surfaces without boundary |
---|---|

Canonical name | GaussBonnetTheoremForSurfacesWithoutBoundary |

Date of creation | 2013-03-22 16:37:30 |

Last modified on | 2013-03-22 16:37:30 |

Owner | Simone (5904) |

Last modified by | Simone (5904) |

Numerical id | 8 |

Author | Simone (5904) |

Entry type | Theorem |

Classification | msc 53A05 |