Curvature analysis of concircular trajectories in doubly warped product manifolds

Fahad Sikander; Tanveer Fatima; Sharief Deshmukh; Ayman Elsharkawy; Fahad Sikander; Tanveer Fatima; Sharief Deshmukh; Ayman Elsharkawy

doi:10.3934/math.20241066

AIMS Mathematics

2024, Volume 9, Issue 8: 21940-21951. doi: 10.3934/math.20241066

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Research article

Curvature analysis of concircular trajectories in doubly warped product manifolds

1.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah-23442, Saudi Arabia, f.sikander@seu.edu.sa
2.
Department of Mathematics and Statistics, College of Sciences, Taibah University, Yanbu-41911, Saudi Arabia, tansari@taibahu.edu.sa
3.
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia, shariefd@ksu.edu.sa
4.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt, ayman_ramadan@science.tanta.edu.eg

Received: 12 March 2024 Revised: 23 June 2024 Accepted: 04 July 2024 Published: 11 July 2024
MSC : 53C22, 53C25, 53C50, 53C80

The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness.
- Hessian tensor,
- Riemann curvature tensor,
- Ricci tensor,
- concircular curvature tensor,
- doubly warped product manifold,
- flat manifold
Citation: Fahad Sikander, Tanveer Fatima, Sharief Deshmukh, Ayman Elsharkawy. Curvature analysis of concircular trajectories in doubly warped product manifolds[J]. AIMS Mathematics, 2024, 9(8): 21940-21951. doi: 10.3934/math.20241066

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Abstract

The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness.

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