this fundamental difference between the two theories can be captured by giving an additional piece of data on the underlying "g"-bundle of a "g"-structure: the solder form. the solder form is what ties the underlying principal bundle of the "g"-structure to the local geometry of the manifold itself by specifying a canonical isomorphism of the tangent bundle of "m" to an associated vector bundle. although the solder form is not a connection form, it can sometimes be regarded as a precursor to one.