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...

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Bibliographic Details
Published in:Mathematics
Main Author: Olga Belova
Format: Text
Language:English
Published: Multidisciplinary Digital Publishing Institute 2019
Subjects:
differentiable manifold
Cartan–Laptev method
space of centered planes
normalization
reduction
connection
laptev
Online Access:https://doi.org/10.3390/math7100901
Description
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 .

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