Editing Pullback (differential geometry) (section)

==Pullback by automorphisms==

The construction of the previous section has a representation-theoretic interpretation when <math>\phi</math> is a diffeomorphism from a manifold <math>M</math> to itself. In this case the derivative <math>d\phi</math> is a section of <math>\operatorname{GM}(TM,\phi^*TM)</math>. This induces a pullback action on sections of any bundle associated to the [[frame bundle]] <math>\operatorname{GM}(m)</math> of <math>M</math> by a representation of the [[general linear group]] <math>\operatorname{GM}(m)</math> (where <math>m = \dim M</math>).