  This article is a continuation of a previous work that dealt with the
topological obstructions to the reductions of the bundle of linear frames on a
spacetime manifold for a particular chain of subgroups of GL(4). In this
article, the corresponding geometrical information, such as connections,
torsion, curvature, and automorphisms of the reductions will be discussed. The
details are elaborated upon for a certain sequence of reductions of GL(M) when
M is a four-dimensional spacetime manifold.
