Spacetime G-structures II: geometry of the ground states
  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. 
David Delphenich