Reduction of Bundles, Connection, Curvature, and Torsion of the Centered Planes Space at Normalization

The space Pi of centered m-planes is considered in projective space P-n. A principal bundle is associated with the space Pi and a group connection is given on the principal bundle. The connection is not uniquely induced at the normalization of the space Pi. Semi-normalized spaces Pi(1), Pi(2) and normalized space Pi(1,2) are investigated. By virtue of the Cartan-Laptev method, the dynamics of changes of corresponding bundles, group connection objects, curvature and torsion of the connections are discovered at a transition from the space Pi to the normalized space Pi(1,2).