# Sub-Riemannian manifold

A *Sub-Riemannian* manifold is a triple $(M,\mathscr{H},{g}_{\mathscr{H}})$ where $M$ is a manifold,
$\mathscr{H}$ is a distribution (that is, a linear subbundle of the tangent bundle^{} $TM$ of $M$), and
${g}_{\mathscr{H}}$ is a metric on $\mathscr{H}$ induced by a fiber inner product on $\mathscr{H}$. The
distribution $\mathscr{H}$ is often referred to as the *horizontal* distribution.

Title | Sub-Riemannian manifold |
---|---|

Canonical name | SubRiemannianManifold |

Date of creation | 2013-03-22 13:58:52 |

Last modified on | 2013-03-22 13:58:52 |

Owner | RevBobo (4) |

Last modified by | RevBobo (4) |

Numerical id | 4 |

Author | RevBobo (4) |

Entry type | Definition |

Classification | msc 53C17 |

Synonym | Sub-Riemannian geometry |