Centered planes in the projective connection space
The space of centered planes is considered in the Cartan projective connection space . The space is important because it has connection with the Grassmann manifold, which plays an important role in geometry and topology, since it is the basic space of a universal vector bundle. The space is an n...
| 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
2020
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| Subjects: | |
| Online Access: | https://doi.org/10.5922/0321-4796-2020-51-4 https://doaj.org/article/047eea12e8234c129b1d8a835e69f592 |
| Summary: | The space of centered planes is considered in the Cartan projective connection space . The space is important because it has connection with the Grassmann manifold, which plays an important role in geometry and topology, since it is the basic space of a universal vector bundle. The space is an n-dimensional differentiable manifold with each point of which an n-dimensional projective space containing this point is associated. Thus, the manifold is the base, and the space is the n-dimensional fiber “glued” to the points of the base. A projective space is a quotient space of a linear space with respect to the equivalence (collinearity) of non-zero vectors, that is . The projective space is a manifold of dimension n. In this paper we use the Laptev — Lumiste invariant analytical method of differential geometric studies of the space of centered planes and introduce a fundamental-group connection in the associated bundle . The bundle contains four quotient bundles. It is show that the connection object is a quasi-tensor containing four subquasi-tensors that define connections in the corresponding quotient bundles. |
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