Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can someone give me an intuitive explanation of the pullback bundle of a vector bundle in differential geometry? You can apply it to the tangent bundle as that's probably easier to visualise.

Am I right that the pullback bundle (where the vector bundle is the tangent bundle) of a map $u: M \to N$ is a subset of the tangent bundle $TN$?

share|improve this question
2  
A vector bundle on $N$ is intuitively a family of vector spaces indexed by points of $N$. If we have a map $f: M \to N$ and a family of vector spaces indexed by points of $N$, we get a family of vector spaces indexed by points of $M$ by attaching to $p \in M$ the vector space attached to $f(p) \in N$. –  user29743 Nov 26 '12 at 15:21
    
(The reason this intuition isn't rigorous is that I need to say the family "varies smoothly" as $n$ varies in $N$, which is why you use the definition of vector bundle that you do (and why we need $f$ to be a smooth map to get a pullback bundle).) –  user29743 Nov 26 '12 at 15:22

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.