Geometric analysis of the pseudo-projective curvature tensor in doubly and twisted warped product manifolds

Ayman Elsharkawy; Hoda Elsayied; Abdelrhman Tawfiq; Fatimah Alghamdi; Ayman Elsharkawy; Hoda Elsayied; Abdelrhman Tawfiq; Fatimah Alghamdi

doi:10.3934/math.2025004

AIMS Mathematics

2025, Volume 10, Issue 1: 56-71. doi: 10.3934/math.2025004

Previous Article Next Article

Research article Topical Sections

Geometric analysis of the pseudo-projective curvature tensor in doubly and twisted warped product manifolds

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt; hkelsayied1998@yahoo.com
2.
Department of Mathematics, Faculty of Education, Ain-Shams University, Cairo, Egypt; abdelrhmanmagdi@edu.asu.edu.eg
3.
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia; fmalghamdi@uj.edu.sa

Received: 22 October 2024 Revised: 16 December 2024 Accepted: 26 December 2024 Published: 02 January 2025
MSC : 53C20, 53C21, 53C25, 53C30, 53C50

This study investigates the pseudo-projective curvature tensor within the framework of doubly and twisted warped product manifolds. It offers significant insights into the interaction between the pseudo-projective curvature tensor and both the base and fiber manifolds. The research highlights key geometric characteristics of the base and fiber manifolds as influenced by the pseudo-projective curvature tensor in these structures. Additionally, the paper extends its analysis to examine the behavior of the pseudo-projective curvature tensor in the context of generalized doubly and twisted generalized Robertson-Walker space-times.
Citation: Ayman Elsharkawy, Hoda Elsayied, Abdelrhman Tawfiq, Fatimah Alghamdi. Geometric analysis of the pseudo-projective curvature tensor in doubly and twisted warped product manifolds[J]. AIMS Mathematics, 2025, 10(1): 56-71. doi: 10.3934/math.2025004

Related Papers:

Abstract

This study investigates the pseudo-projective curvature tensor within the framework of doubly and twisted warped product manifolds. It offers significant insights into the interaction between the pseudo-projective curvature tensor and both the base and fiber manifolds. The research highlights key geometric characteristics of the base and fiber manifolds as influenced by the pseudo-projective curvature tensor in these structures. Additionally, the paper extends its analysis to examine the behavior of the pseudo-projective curvature tensor in the context of generalized doubly and twisted generalized Robertson-Walker space-times.

References

[1]	R. L. Bishop, B. O'Neill, Geometry of slant submanifolds, Trans. Amer. Math. Soc., 145 (1969).
[2]	S. Nölker, Isometric immersions of warped products, Differ. Geom. Appl., 6 (1996), 1–30. https://doi.org/10.1016/0926-2245(96)00004-6 doi: 10.1016/0926-2245(96)00004-6
[3]	P. E. Ehrlich, Metric deformations of Ricci and sectional curvature on compact Riemannian manifolds, Ph. D. thesis, State University of New York at Stony Brook, 1974.
[4]	A. M. Blaga, C. Özgür, Killing and 2-Killing vector fields on doubly warped products, Mathematics, 11 (2023), 4983. https://doi.org/10.3390/math11244983 doi: 10.3390/math11244983
[5]	H. K. El-Sayied, S. Shenawy, N. Syied, Conformal vector fields on doubly warped product manifolds and applications, Adv. Math. Phys., 1 (2016), 1–11. https://doi.org/10.1155/2016/6508309 doi: 10.1155/2016/6508309
[6]	H. K. Elsayied, A. M. Tawfiq, A. Elsharkawy, Some characterizations of quasi-Einstein and doubly product manifold, Int. J. Geom. Methods Mod. Phys., 21 (2024), 2450165. https://doi.org/10.1142/S0219887824501652 doi: 10.1142/S0219887824501652
[7]	F. Karaca, C. Özgür, Gradient Ricci-harmonic solitons on doubly warped product manifolds, Filomat, 37 (2023), 5969–5977. https://doi.org/10.2298/fil2318969k doi: 10.2298/fil2318969k
[8]	F. Sikander, T. Fatima, S. Deshmukh, A. Elsharkawy, Curvature analysis of concircular trajectories in doubly warped product manifolds, AIMS Math., 9 (2024), 21940–21951. https://doi.org/10.3934/math.20241066 doi: 10.3934/math.20241066
[9]	B. Ünal, Doubly warped products, Differ. Geom. Appl., 15 (2001), 253–263. https://doi.org/10.1016/S0926-2245(01)00051-1 doi: 10.1016/S0926-2245(01)00051-1
[10]	B. Chen, Geometry of submanifolds and its applications, Science University of Tokyo, 1981.
[11]	B. Prasad, A pseudo-projective curvature tensor on a Riemannian manifold, Bull. Cal. Math. Soc., 94 (2002), 163–166.
[12]	Y. Dogru, Hypersurfaces satisfying some curvature conditions on pseudo projective curvature tensor in the semi-Euclidean space, Math. Sci. Appl. E-Notes, 2, (2014), 99–105. https://doi.org/10.36753/MATHENOT.207636 doi: 10.36753/MATHENOT.207636
[13]	J. P. Jaiswal, R. H. Ojha, On weakly pseudo-projectively symmetric manifolds, Differ. Geom. Dyn. Syst., 12 (2010), 83–94.
[14]	H. G. Nagaraja, G. Somashekhara, On pseudo projective curvature tensor in Sasakian manifolds, Int. J. Contemp. Math. Sci., 6 (2011), 1319–1328.
[15]	S. Shenawy, B. Ünal, The $W_2$-curvature tensor on warped product manifolds and applications, Int. J. Geom. Methods Mod. Phys., 13 (2016), 1650099. https://doi.org/10.1142/S0219887816500997 doi: 10.1142/S0219887816500997
[16]	D. Narain, A. Prakash, B. Prasad, A pseudo projective curvature tensor on Lorentzian para-Sasakian manifold, An. Stiint. Univ., 55 (2009), 275–284.

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)