Symmetries in Riemann-Cartan Geometries
Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics, including quantum gravity theories, and have many important differences when compared to Riemannian geometrie...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212342 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Symmetries in Riemann-Cartan Geometries. David D. McNutt, Alan A. Coley and Robert J. van den Hoogen. SIGMA 20 (2024), 078, 20 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707745151516672 |
|---|---|
| author | McNutt, David D. Coley, Alan A. van den Hoogen, Robert J. |
| author_facet | McNutt, David D. Coley, Alan A. van den Hoogen, Robert J. |
| citation_txt | Symmetries in Riemann-Cartan Geometries. David D. McNutt, Alan A. Coley and Robert J. van den Hoogen. SIGMA 20 (2024), 078, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics, including quantum gravity theories, and have many important differences when compared to Riemannian geometries. One notable difference is that the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.
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| first_indexed | 2026-03-19T04:56:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212342 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T04:56:40Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | McNutt, David D. Coley, Alan A. van den Hoogen, Robert J. 2026-02-05T09:53:38Z 2024 Symmetries in Riemann-Cartan Geometries. David D. McNutt, Alan A. Coley and Robert J. van den Hoogen. SIGMA 20 (2024), 078, 20 pages 1815-0659 2020 Mathematics Subject Classification: 53A55; 83D99; 53Z05 arXiv:2401.00780 https://nasplib.isofts.kiev.ua/handle/123456789/212342 https://doi.org/10.3842/SIGMA.2024.078 Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics, including quantum gravity theories, and have many important differences when compared to Riemannian geometries. One notable difference is that the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries. The authors would like to thank the anonymous referees for their helpful comments, which have improved the quality of the paper. AAC and RvdH are supported by the Natural Sciences and Engineering Research Council of Canada. RvdH is supported by the Dr. W.F. James Chair of Studies in the Pure and Applied Sciences at St. Francis Xavier University. DDM is supported by the Norwegian Financial Mechanism 2014-2021 (project registration number 2019/34/H/ST1/00636). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries in Riemann-Cartan Geometries Article published earlier |
| spellingShingle | Symmetries in Riemann-Cartan Geometries McNutt, David D. Coley, Alan A. van den Hoogen, Robert J. |
| title | Symmetries in Riemann-Cartan Geometries |
| title_full | Symmetries in Riemann-Cartan Geometries |
| title_fullStr | Symmetries in Riemann-Cartan Geometries |
| title_full_unstemmed | Symmetries in Riemann-Cartan Geometries |
| title_short | Symmetries in Riemann-Cartan Geometries |
| title_sort | symmetries in riemann-cartan geometries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212342 |
| work_keys_str_mv | AT mcnuttdavidd symmetriesinriemanncartangeometries AT coleyalana symmetriesinriemanncartangeometries AT vandenhoogenrobertj symmetriesinriemanncartangeometries |