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Results tagged with vector-bundles
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user 39404
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
1
vote
Why do we use the less simple convention for the definition of a vector bundle connection?
The "usual" definition tantamounts to saying that $[\nabla, \omega ]=d\omega$, where $[,]$ is the (graded) commutator of (graded) endomorphisms.
- 153
4
votes
2
answers
541
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Existence of connections making a bundle endomorphism parallel
Let $M$ be a manifold, $TM$ its tangent bundle, and $N:TM\to TM$ a vector bundle morphism. It is possible to find a torsionless linear connection $\nabla$ on $TM$ such that $\nabla N=0$?
- 153