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

Abstract

The space Π of centered m-planes is considered in projective space Pn. A principal bundle isassociated with the space Π and a group connection is given on the principal bundle. The connectionis not uniquely induced at the normalization of the space Π. Semi-normalized spaces Π1, Π2 andnormalized space Π1,2 are investigated. By virtue of the Cartan–Laptev method, the dynamics ofchanges of corresponding bundles, group connection objects, curvature and torsion of the connectionsare discovered at a transition from the space Π to the normalized space Π1,2.