Reduction of Bundles, Connection, Curvature, and Torsion of the Centered Planes Space at Normalization
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 normal...
Published in: | Mathematics |
---|---|
Main Author: | |
Format: | Text |
Language: | English |
Published: |
Multidisciplinary Digital Publishing Institute
2019
|
Subjects: | |
Online Access: | https://doi.org/10.3390/math7100901 |
Summary: | 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 . |
---|