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

Olga Belova
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Olga Belova: Institute of Physical and Mathematical Sciences and IT, Immanuel Kant Baltic Federal University, A. Nevsky str. 14, 236016 Kaliningrad, Russia

Mathematics, 2019, vol. 7, issue 10, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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