subbundle

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

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

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

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

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

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