Glued linear connection on surface of the projective space
We consider a surface as a variety of centered planes in a multidimensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle. We called it a glued bundle of the linear coframes. A connection...
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| Format: | Article |
| Language: | English |
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Immanuel Kant Baltic Federal University
2020-08-01
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| Series: | Дифференциальная геометрия многообразий фигур |
| Subjects: | |
| Online Access: | https://journals.kantiana.ru/geometry/4686/25774/ |
| _version_ | 1828863876278517760 |
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| author | K.V. Bashashina |
| author_facet | K.V. Bashashina |
| author_sort | K.V. Bashashina |
| collection | DOAJ |
| description | We consider a surface as a variety of centered planes in a multidimensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle. We called it a glued bundle of the linear coframes. A connection is set by the Laptev — Lumiste method in the fiber bundle. The ifferential equations of the connection object components have been found. This leads to a space of the glued linear connection. The expressions for a curvature object of the given connection are found in the paper. The theorem is proved that the curvature object is a tensor. A condition is found under which the space of the glued linear connection turns into the space of Cartan projective connection. The study uses the Cartan — Laptev method, which is based on calculating external differential forms. Moreover, all considerations in the article have a local manner.
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| first_indexed | 2024-12-13T03:53:31Z |
| format | Article |
| id | doaj.art-abdc193ce7da400b889ec19cf9870328 |
| institution | Directory Open Access Journal |
| issn | 0321-4796 2782-3229 |
| language | English |
| last_indexed | 2024-12-13T03:53:31Z |
| publishDate | 2020-08-01 |
| publisher | Immanuel Kant Baltic Federal University |
| record_format | Article |
| series | Дифференциальная геометрия многообразий фигур |
| spelling | doaj.art-abdc193ce7da400b889ec19cf98703282022-12-22T00:00:39ZengImmanuel Kant Baltic Federal UniversityДифференциальная геометрия многообразий фигур0321-47962782-32292020-08-0151222810.5922/0321-4796-2020-51-3Glued linear connection on surface of the projective space K.V. Bashashina0https://orcid.org/0000-0002-7209-884XImmanuel Kant Baltic Federal UniversityWe consider a surface as a variety of centered planes in a multidimensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle. We called it a glued bundle of the linear coframes. A connection is set by the Laptev — Lumiste method in the fiber bundle. The ifferential equations of the connection object components have been found. This leads to a space of the glued linear connection. The expressions for a curvature object of the given connection are found in the paper. The theorem is proved that the curvature object is a tensor. A condition is found under which the space of the glued linear connection turns into the space of Cartan projective connection. The study uses the Cartan — Laptev method, which is based on calculating external differential forms. Moreover, all considerations in the article have a local manner. https://journals.kantiana.ru/geometry/4686/25774/projective space surfaceglued bundlelinear connectionglued linear connectioncartan projective connectioncurvature tensor |
| spellingShingle | K.V. Bashashina Glued linear connection on surface of the projective space Дифференциальная геометрия многообразий фигур projective space surface glued bundle linear connection glued linear connection cartan projective connection curvature tensor |
| title | Glued linear connection on surface of the projective space |
| title_full | Glued linear connection on surface of the projective space |
| title_fullStr | Glued linear connection on surface of the projective space |
| title_full_unstemmed | Glued linear connection on surface of the projective space |
| title_short | Glued linear connection on surface of the projective space |
| title_sort | glued linear connection on surface of the projective space |
| topic | projective space surface glued bundle linear connection glued linear connection cartan projective connection curvature tensor |
| url | https://journals.kantiana.ru/geometry/4686/25774/ |
| work_keys_str_mv | AT kvbashashina gluedlinearconnectiononsurfaceoftheprojectivespace |