Generalized bilinear connection on the space of centered planes
We continue to study the space of centered planes in projective space . In this paper, we use E. Cartan's method of external forms and the group-theoretical method of G. F. Laptev to study the space of centered planes of the same dimension. These methods are successfully applied in physics. In...
| Published in: | Differential Geometry of Manifolds of Figures |
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| Main Author: | |
| Format: | Article in Journal/Newspaper |
| Language: | English Russian |
| Published: |
Immanuel Kant Baltic Federal University
2022
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| Subjects: | |
| Online Access: | https://doi.org/10.5922/0321-4796-2022-53-3 https://doaj.org/article/f9b3bd0e4e9b481a8faa5188fab1a601 |
| Summary: | We continue to study the space of centered planes in projective space . In this paper, we use E. Cartan's method of external forms and the group-theoretical method of G. F. Laptev to study the space of centered planes of the same dimension. These methods are successfully applied in physics. In a generalized bundle, a bilinear connection associated with a space is given. The connection object contains two simplest subtensors and subquasi-tensors (four simplest and three simple subquasi-tensors). The object field of this connection defines the objects of torsion, curvature-torsion, and curvature. The curvature tensor contains six simplest and four simple subtensors, and curvature-torsion tensor contains three simplest and two simple subtensors. The canonical case of a generalized bilinear connection is considered. |
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