Warped product manifolds: Characterizations through the symmetry of the semiconformal curvature tensor and applications

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This paper investigates the impact of the semiconformal curvature tensor’s symmetry on the base and fiber manifolds of a warped product manifold. It establishes that the fiber manifold of a warped product manifold has a constant sectional curvature, whereas the base manifold is semiconformally symmetric. Furthermore, the paper derives the specific forms of the semiconformal curvature tensor for both the base and fiber manifolds. Also, it is demonstrated that a semiconformally symmetric (flat) GRW space-time is a perfect fluid space-time and exhibits an irrotational velocity vector field.