Characterization of warped product manifolds through the W2-curvature tensor with applications to relativity
Abdallah Abdelhameed Syied,
Uday Chand De,
Nasser Bin Turki,
Gabriel-Eduard Vîlcu
Affiliations
Abdallah Abdelhameed Syied
Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt; Corresponding author.
Uday Chand De
Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road Kolkata 700019, West Bengal, India
Nasser Bin Turki
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Gabriel-Eduard Vîlcu
“Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania; National University of Science and Technology Politehnica Bucharest, Faculty of Applied Sciences, Department of Mathematics and Informatics, 313 Splaiul Independenţei, 060042 Bucharest, Romania
We first investigate how the flatness and the symmetry of the W2-tensor impact both the base manifold and the fiber manifold of a warped product manifold. In both cases, we determine the form of the W2-tensor on both the fiber and the base manifolds. Additionally, we establish that the fiber manifold is of constant curvature, while the base manifold is Einstein. It is also proved that a W2-curvature flat GRW space-time is perfect fluid and static. Furthermore, the space-time either represents dark matter era or the state equation has a specific form.
