A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds
The main aim of this study is to investigate the effects of the P−curvature flatness, P−divergence-free characteristic, and P−symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P−curvature flat warped manifold are...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7882356 |
| _version_ | 1826998730676502528 |
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| author | Uday Chand De Abdallah Abdelhameed Syied Nasser Bin Turki Suliman Alsaeed |
| author_facet | Uday Chand De Abdallah Abdelhameed Syied Nasser Bin Turki Suliman Alsaeed |
| author_sort | Uday Chand De |
| collection | DOAJ |
| description | The main aim of this study is to investigate the effects of the P−curvature flatness, P−divergence-free characteristic, and P−symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P−curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P−curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P−divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P−symmetric warped product manifold is considered. |
| first_indexed | 2024-04-11T20:42:51Z |
| format | Article |
| id | doaj.art-c1273cc9a54f4471894d0ac0c0b9150c |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2025-02-18T10:18:50Z |
| publishDate | 2021-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-c1273cc9a54f4471894d0ac0c0b9150c2024-11-02T05:31:45ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/7882356A Study of Generalized Projective P−Curvature Tensor on Warped Product ManifoldsUday Chand De0Abdallah Abdelhameed Syied1Nasser Bin Turki2Suliman Alsaeed3Department of Pure MathematicsDepartment of MathematicsDepartment of MathematicsApplied Science CollegeThe main aim of this study is to investigate the effects of the P−curvature flatness, P−divergence-free characteristic, and P−symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P−curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P−curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P−divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P−symmetric warped product manifold is considered.http://dx.doi.org/10.1155/2021/7882356 |
| spellingShingle | Uday Chand De Abdallah Abdelhameed Syied Nasser Bin Turki Suliman Alsaeed A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds Journal of Mathematics |
| title | A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds |
| title_full | A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds |
| title_fullStr | A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds |
| title_full_unstemmed | A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds |
| title_short | A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds |
| title_sort | study of generalized projective p curvature tensor on warped product manifolds |
| url | http://dx.doi.org/10.1155/2021/7882356 |
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