Let \((E,\pi,M)\) be a vector fiber bundle . It is called smooth if \(E\) and \(M\) are [smooth manifolds](smooth manifold.md), \(\pi\) a smooth map between \(E\) and \(M\) and the local trivialization can be chosen as a diffeomorphism.
Let \((E,\pi,M)\) be a vector fiber bundle . It is called smooth if \(E\) and \(M\) are [smooth manifolds](smooth manifold.md), \(\pi\) a smooth map between \(E\) and \(M\) and the local trivialization can be chosen as a diffeomorphism.