Conharmonically flat and conharmonically symmetric warped product manifolds
This article presents characterizations of warped product manifolds based on the flatness and symmetry of the conharmonic curvature tensor. It is proved that when a warped product manifold is conharmonically flat, both the base and fiber manifolds exhibit constant sectional curvatures. In addition,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2024-03-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0197961 |
| _version_ | 1797227600359194624 |
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| author | Abdallah Abdelhameed Syied Uday Chand De Nasser Bin Turki |
| author_facet | Abdallah Abdelhameed Syied Uday Chand De Nasser Bin Turki |
| author_sort | Abdallah Abdelhameed Syied |
| collection | DOAJ |
| description | This article presents characterizations of warped product manifolds based on the flatness and symmetry of the conharmonic curvature tensor. It is proved that when a warped product manifold is conharmonically flat, both the base and fiber manifolds exhibit constant sectional curvatures. In addition, the specific forms of the conharmonic curvature tensor are derived for both the base and fiber manifolds. It is demonstrated that in a conharmonically symmetric warped product manifold, the fiber manifold has a constant sectional curvature, while the base manifold is both Cartan-symmetric and conharmonically symmetric. In this scenario, the form of the conharmonic curvature tensor on the fiber manifold is determined. We characterize the generalized Robertson–Walker (GRW) space-time through the flatness and the symmetry of the conharmonic curvature tensor. It is shown that a conharmonically flat (symmetric) GRW space-time is a perfect fluid. Finally, a conharmonically flat standard static space-time is investigated. |
| first_indexed | 2024-04-24T14:43:23Z |
| format | Article |
| id | doaj.art-fd8e32e93a9745818baa3528b7faa490 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-04-24T14:43:23Z |
| publishDate | 2024-03-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-fd8e32e93a9745818baa3528b7faa4902024-04-02T20:29:18ZengAIP Publishing LLCAIP Advances2158-32262024-03-01143035322035322-1310.1063/5.0197961Conharmonically flat and conharmonically symmetric warped product manifoldsAbdallah Abdelhameed Syied0Uday Chand De1Nasser Bin Turki2Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, EgyptDepartment of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, IndiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThis article presents characterizations of warped product manifolds based on the flatness and symmetry of the conharmonic curvature tensor. It is proved that when a warped product manifold is conharmonically flat, both the base and fiber manifolds exhibit constant sectional curvatures. In addition, the specific forms of the conharmonic curvature tensor are derived for both the base and fiber manifolds. It is demonstrated that in a conharmonically symmetric warped product manifold, the fiber manifold has a constant sectional curvature, while the base manifold is both Cartan-symmetric and conharmonically symmetric. In this scenario, the form of the conharmonic curvature tensor on the fiber manifold is determined. We characterize the generalized Robertson–Walker (GRW) space-time through the flatness and the symmetry of the conharmonic curvature tensor. It is shown that a conharmonically flat (symmetric) GRW space-time is a perfect fluid. Finally, a conharmonically flat standard static space-time is investigated.http://dx.doi.org/10.1063/5.0197961 |
| spellingShingle | Abdallah Abdelhameed Syied Uday Chand De Nasser Bin Turki Conharmonically flat and conharmonically symmetric warped product manifolds AIP Advances |
| title | Conharmonically flat and conharmonically symmetric warped product manifolds |
| title_full | Conharmonically flat and conharmonically symmetric warped product manifolds |
| title_fullStr | Conharmonically flat and conharmonically symmetric warped product manifolds |
| title_full_unstemmed | Conharmonically flat and conharmonically symmetric warped product manifolds |
| title_short | Conharmonically flat and conharmonically symmetric warped product manifolds |
| title_sort | conharmonically flat and conharmonically symmetric warped product manifolds |
| url | http://dx.doi.org/10.1063/5.0197961 |
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