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 P n . A principal bundle is associated with the space Π and a group connection is given on the principal bundle. The connection is not uniquely induced at the normalization of the space Π . Semi-normalized spaces Π 1 , Π 2 and normalized space Π 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 Π to the normalized space Π 1 , 2 .

Keywords

• differentiable manifold
• cartan–laptev method
• space of centered planes
• normalization
• reduction
• connection