Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications
Source abstract
Abstract
This paper introduces a description of a doubly warped product manifold, taking into account certain conditions related to the projective curvature tensor. We demonstrate that the factor manifolds of a projectively flat (symmetric) doubly warped product manifold possess constant sectional curvature. In the flatness scenario, a doubly warped product manifold reduces to a singly warped product manifold. We establish that the factor manifolds of a doubly warped product manifold with harmonic projective curvature tensor are Einstein manifolds and exhibit harmonic projective curvature tensor. In Sec. VI, we provide evidence that a projectively flat (symmetric) generalized Robertson–Walker space-time is both a perfect fluid and static.
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Research context
OpenAlex topics: Geometric Analysis and Curvature Flows · Astrophysical Phenomena and Observations · Cosmology and Gravitation Theories
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Faculty of Science, Zagazig University 1 , P.O. Box 44519, Zagazig, Egypt
Department of Pure Mathematics, University of Calcutta 2 , 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India
Department of Mathematics, College of Science, King Saud University 3 , P.O. Box 2455, Riyadh 11451, Saudi Arabia
Department of Mathematics, Pachhunga University College 4 , Aizawl, Mizoram, India
Funding
Deanship of Scientific Research, King Saud University
References (28)
Show source-provided references
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