The Mathematical Heritage of C F Gauss

... preserves the structure of {FIa} must be non-homogeneous with components in
distinct cotangent spaces of G. By means of such pre-gauge transformations the
exterior derivatives of the matrices of the adjoint representation of G can be
decomposed to yield a theory of connections and curvature on G that is distinct
from any theory of affine connections. It is subsequently assumed that the group
parameters are functions of the coordinates of a given base manifold M. This
gives rise to ...