Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds

Author:

Shenawy Sameh1ORCID,De Uday Chand2ORCID,Bin Turki Nasser3ORCID,Pundeer Naeem Ahmad4ORCID

Affiliation:

1. Basic Science Department, Modern Academy for Engineering and Technology, Maadi 11585, Egypt

2. Department of Pure Mathematics, University of Calcutta 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India

3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

4. Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India

Abstract

The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ=ζ1+ζ2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse’s problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference32 articles.

1. Aazami, A.B., and Ream, R. (2023). Killing vector fields on Riemannian and Lorentzian 3-manifolds. Math. Nachrichten, in press.

2. Duggal, K.L., and Sharma, R. (2013). Symmetries of Spacetimes and Riemannian Manifolds, Springer Science & Business Media.

3. Hall, G.S. (2004). Symmetries and Curvature Structure in General Relativity, World Scientific.

4. Besse, A.L. (2008). Einstein Manifolds, Springer.

5. GRAY’s Decomposition and Warped Product of Generalized Ricci Recurrent Spacetimes;De;Rep. Math. Phys.,2023

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