A Manifold defined over another Manifold with a projection whose fibers are Vector spaces.

See definition here.

Generalizes constructions like the Tangent bundle

Algebraic operations on vector bundles

Can generalize a lot of algebraic operations on Vector spaces to Vector bundles over manifolds. In particular, we can generalize:

• Dual vector space
• Direct sum
• Tensor product
• Wedge product

The fibers of all these vector bundles correspond to the corresponding vector space operations on the fiber of the original vector bundles.

Videos here

Book here

Pullback of vector bundle (Se here)