On conformally reducible pseudo-Riemannian spaces
The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. T...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2021-09-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/2097 |
| _version_ | 1811228432693985280 |
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| author | Тетяна Iванiвна Шевченко Тетяна Сергіївна Спічак Дмитро Миколайович Дойков |
| author_facet | Тетяна Iванiвна Шевченко Тетяна Сергіївна Спічак Дмитро Миколайович Дойков |
| author_sort | Тетяна Iванiвна Шевченко |
| collection | DOAJ |
| description | The present paper studies the main type of conformal reducible conformally flat spaces.
We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping.
This allows to carry out the complete classification of these spaces.
The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity.
Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces.
Research is carried out locally in tensor shape. |
| first_indexed | 2024-04-12T09:58:53Z |
| format | Article |
| id | doaj.art-b97abb3473cd48b19e145a0d39a94140 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-04-12T09:58:53Z |
| publishDate | 2021-09-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-b97abb3473cd48b19e145a0d39a941402022-12-22T03:37:37ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062021-09-0114215416310.15673/tmgc.v14i2.20972097On conformally reducible pseudo-Riemannian spacesТетяна Iванiвна Шевченко0Тетяна Сергіївна Спічак1Дмитро Миколайович Дойков2Odesa State Academy of Civil Engineering and ArchitectureKherson State Maritime AcademyOdesa National Maritime UniversityThe present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.https://journals.onaft.edu.ua/index.php/geometry/article/view/2097pseudo-riemannian spaces; conformal reducible spaces; conformally flat spaces; subprojective spaces of kagan. |
| spellingShingle | Тетяна Iванiвна Шевченко Тетяна Сергіївна Спічак Дмитро Миколайович Дойков On conformally reducible pseudo-Riemannian spaces Pracì Mìžnarodnogo Geometričnogo Centru pseudo-riemannian spaces; conformal reducible spaces; conformally flat spaces; subprojective spaces of kagan. |
| title | On conformally reducible pseudo-Riemannian spaces |
| title_full | On conformally reducible pseudo-Riemannian spaces |
| title_fullStr | On conformally reducible pseudo-Riemannian spaces |
| title_full_unstemmed | On conformally reducible pseudo-Riemannian spaces |
| title_short | On conformally reducible pseudo-Riemannian spaces |
| title_sort | on conformally reducible pseudo riemannian spaces |
| topic | pseudo-riemannian spaces; conformal reducible spaces; conformally flat spaces; subprojective spaces of kagan. |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/2097 |
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