Pullback (differential Geometry) - Pullback By Automorphisms

Pullback By Automorphisms

The construction of the previous section has a representation-theoretic interpretation when φ is a diffeomorphism from a manifold M to itself. In this case the derivative dφ is a section of GL(TM,φ*TM). This induces a pullback action on sections of any bundle associated to the frame bundle GL(M) of M by a representation of the general linear group GL(m) (m = dim M).