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,...

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Bibliographic Details
Published in:AIP advances 2024-03, Vol.14 (3), p.035322-035322-13
Main Authors: Syied, Abdallah Abdelhameed, Chand De, Uday, Turki, Nasser Bin
Format: Article
Language:English
Subjects:
Curvature
Flatness
Manifolds
Mathematical analysis
Symmetry
Tensors
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Summary: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.
ISSN:2158-3226
2158-3226
DOI:10.1063/5.0197961