Definition:Smooth Vector Bundle
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Definition
Let $B = \tuple {E, M, \pi, F}$ be a smooth fiber bundle.
Let $F$ be a vector space.
Let vector addition and scalar multiplication on $F$ be smooth.
Then $B$ is a smooth vector bundle over $M$.
Also see
Sources
- 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 10$: Vector Bundles