# subbundle

Given a vector bundle^{} $\pi :\mathcal{E}\to M$, a subbundle ${\mathcal{E}}^{\prime}$ is a subset of the total space, ${\mathcal{E}}^{\prime}\subset \mathcal{E}$, so that

$${\pi |}_{{\mathcal{E}}^{\prime}}:{\mathcal{E}}^{\prime}\to M$$ |

is a vector bundle, and for each point $p\in M$, the fibre at $p$

$$\pi |_{{\mathcal{E}}^{\prime}}{}^{-1}(p)={\mathcal{E}}_{p}^{\prime}$$ |

is a vector subspace of ${\mathcal{E}}_{p}={\pi}^{-1}(p)$

Title | subbundle |

Canonical name | Subbundle |

Date of creation | 2013-03-22 16:50:54 |

Last modified on | 2013-03-22 16:50:54 |

Owner | guffin (12505) |

Last modified by | guffin (12505) |

Numerical id | 4 |

Author | guffin (12505) |

Entry type | Definition |

Classification | msc 14F05 |

Classification | msc 55R25 |

Synonym | sub-bundle |

Synonym | vector sub-bundle |

Synonym | vector subbundle |

Synonym | sub-vector bundle |

Synonym | sub vector bundle |

Defines | subbundle |