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 |
---|---|
Main Author: | |
Format: | Article in Journal/Newspaper |
Language: | English Russian |
Published: |
Immanuel Kant Baltic Federal University
2021
|
Subjects: | |
Online Access: | https://doi.org/10.5922/0321-4796-2021-52-4 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 |
id |
ftdoajarticles:oai:doaj.org/article:25ca7e25b5d04cf389f9d7c1f50dad03 |
---|---|
record_format |
openpolar |
spelling |
ftdoajarticles:oai:doaj.org/article:25ca7e25b5d04cf389f9d7c1f50dad03 2023-05-15T17:07:17+02:00 The Grassmann-like manifold of centered planes when a surface is described by the centre O.O. Belova 2021-08-01T00:00:00Z https://doi.org/10.5922/0321-4796-2021-52-4 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 EN RU eng rus Immanuel Kant Baltic Federal University https://journals.kantiana.ru/geometry/4985/32683/ https://doaj.org/toc/0321-4796 https://doaj.org/toc/2782-3229 doi:10.5922/0321-4796-2021-52-4 0321-4796 2782-3229 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 Дифференциальная геометрия многообразий фигур, Iss 52, Pp 30-41 (2021) projective space the grassmann-like manifold surface connection parallel displacements Mathematics QA1-939 article 2021 ftdoajarticles https://doi.org/10.5922/0321-4796-2021-52-4 2022-12-31T04:09:29Z 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. Article in Journal/Newspaper laptev Directory of Open Access Journals: DOAJ Articles Differential Geometry of Manifolds of Figures 52 30 41 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English Russian |
topic |
projective space the grassmann-like manifold surface connection parallel displacements Mathematics QA1-939 |
spellingShingle |
projective space the grassmann-like manifold surface connection parallel displacements Mathematics QA1-939 O.O. Belova The Grassmann-like manifold of centered planes when a surface is described by the centre |
topic_facet |
projective space the grassmann-like manifold surface connection parallel displacements Mathematics QA1-939 |
description |
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. |
format |
Article in Journal/Newspaper |
author |
O.O. Belova |
author_facet |
O.O. Belova |
author_sort |
O.O. Belova |
title |
The Grassmann-like manifold of centered planes when a surface is described by the centre |
title_short |
The Grassmann-like manifold of centered planes when a surface is described by the centre |
title_full |
The Grassmann-like manifold of centered planes when a surface is described by the centre |
title_fullStr |
The Grassmann-like manifold of centered planes when a surface is described by the centre |
title_full_unstemmed |
The Grassmann-like manifold of centered planes when a surface is described by the centre |
title_sort |
grassmann-like manifold of centered planes when a surface is described by the centre |
publisher |
Immanuel Kant Baltic Federal University |
publishDate |
2021 |
url |
https://doi.org/10.5922/0321-4796-2021-52-4 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 |
genre |
laptev |
genre_facet |
laptev |
op_source |
Дифференциальная геометрия многообразий фигур, Iss 52, Pp 30-41 (2021) |
op_relation |
https://journals.kantiana.ru/geometry/4985/32683/ https://doaj.org/toc/0321-4796 https://doaj.org/toc/2782-3229 doi:10.5922/0321-4796-2021-52-4 0321-4796 2782-3229 https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03 |
op_doi |
https://doi.org/10.5922/0321-4796-2021-52-4 |
container_title |
Differential Geometry of Manifolds of Figures |
container_issue |
52 |
container_start_page |
30 |
op_container_end_page |
41 |
_version_ |
1766062653706338304 |