# Gaussian curvature

The *Gaussian curvature ^{}* of a surface at a point $p$ is the product

$$K={\kappa}_{1}{\kappa}_{2}$$ |

of the two principal curvatures^{} of the surface at $p$.

The arithmetic mean^{} of the principal curvatures at a point $p$

$$H=\frac{{\kappa}_{1}+{\kappa}_{2}}{2}$$ |

is called the *mean curvature ^{}* of the surface at
$p$.

Title | Gaussian curvature |
---|---|

Canonical name | GaussianCurvature |

Date of creation | 2013-03-22 17:00:56 |

Last modified on | 2013-03-22 17:00:56 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 6 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 53A05 |

Synonym | total curvature |

Synonym | total normal curvature |

Related topic | MeanCurvatureAtSurfacePoint |

Defines | mean curvature |