# subbundle

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

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

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

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

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