Pullbacks and Pushforwards Clause Samples

Pullbacks and Pushforwards. Maps from one manifold to another can also be used to relate the vector fields and one-form fields on one manifold to those on the other. We have introduced two such relations: restricted vector fields and the differential of a function. However, there are other ways to relate the vector fields and form fields on different manifolds that are connected by a map. Pullback and Pushforward of a Function The pullback of a function f on M over the map μ is defined as μ∗f = f ◦ μ. (6.10)