The composite equipment for manifold of hypercentered planes, whose dimension coincides with dimension of generating plane
In n-dimensional projective space Pn a manifold , i. e., a family of pairs of planes one of which is a hyperplane in the other, is considered. A principal bundle arises over it, . A typical fiber is the stationarity subgroup of the generator of pair of planes: external plane and its multidimensiona...
| Published in: | Differential Geometry of Manifolds of Figures |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English Russian |
| Published: |
Immanuel Kant Baltic Federal University
2021
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| Subjects: | |
| Online Access: | https://doi.org/10.5922/0321-4796-2021-52-6 https://doaj.org/article/200119ab64fa4d3881139286180a3648 |
| Summary: | In n-dimensional projective space Pn a manifold , i. e., a family of pairs of planes one of which is a hyperplane in the other, is considered. A principal bundle arises over it, . A typical fiber is the stationarity subgroup of the generator of pair of planes: external plane and its multidimensional center — hyperplane. The principal bundle contains four factor-bundles. A fundamental-group connection is set by the Laptev — Lumiste method in the associated fibering. It is shown that the connection object contains four subobjects that define connections in the corresponding factor-bundles. It is proved that the curvature object of fundamental-group connection forms pseudotensor. It contains four subpseudotensors, which are curvature objects of the corresponding subconnections. The composite equipment of the family of hypercentered planes set by means of a point lying in the plane and not belonging to its hypercenter and an (n – m – 1)-dimensional plane, which does not have common points with the hypercentered plane. It is proved, that composite equipment induces the fundamental-group connections of two types in the associated fibering. |
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