in detail, suppose that "q" is the principal bundle of a "g"-structure. if "q" is realized as a reduction of the frame bundle of "m", then the solder form is given by the pullback of the tautological form of the frame bundle along the inclusion. abstractly, if one regards "q" as a principal bundle independently of its realization as a reduction of the frame bundle, then the solder form consists of a representation ρ of "g" on r and an isomorphism of bundles θ : "tm" → "q" × r.