The Grassmann-like manifold of centered planes when a surface is described by the centre
We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center describes an -dimensional surface . We will denote this manifold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalizati...
| 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
2021
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| Subjects: | |
| Online Access: | https://doi.org/10.5922/0321-4796-2021-52-4 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 |
| Summary: | We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center describes an -dimensional surface . We will denote this manifold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalization induces a connection in the bundle associated with the manifold . A geometric characteristic of this connection is given with the help of parallel displacements. In our research we use the Cartan method of external forms and the group-theoretical method of Laptev. These methods are used by many geometers and physicists. The Grassmann-like manifold is closely related to such a well-known and popular manifold as the Grassmann manifold. The Grassmann manifold is an example of a homogeneous space and forms an important fundamental class of projective manifolds, and the projective space itself can be represented as a Grassmann manifold. |
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