On Riemannian warped-twisted product submersions

Richa Agarwal; Fatemah Mofarreh; Sarvesh Kumar Yadav; Shahid Ali; Abdul Haseeb; Richa Agarwal; Fatemah Mofarreh; Sarvesh Kumar Yadav; Shahid Ali; Abdul Haseeb

doi:10.3934/math.2024144

AIMS Mathematics

2024, Volume 9, Issue 2: 2925-2937. doi: 10.3934/math.2024144

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On Riemannian warped-twisted product submersions

1.
Department of Mathematics, Faculty of Sciences, Aligarh Muslim University, Aligarh-202002, India
2.
Mathematical Science Department, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh-11546, Kingdom of Saudi Arabia
3.
Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi-110025, India
4.
Department of Mathematics, College of Science, Jazan University, Jazan-45142, Kingdom of Saudi Arabia

Received: 24 August 2023 Revised: 26 November 2023 Accepted: 06 December 2023 Published: 02 January 2024
MSC : 53C15, 53C40, 53C50

In this paper, we introduce the concepts of Riemannian warped-twisted product submersions and examine their fundamental properties, including total geodesicity, total umbilicity and minimality. Additionally, we investigate the Ricci tensor of Riemannian warped-twisted product submersions, specifically about the horizontal and vertical distributions. Finally, we obtain Einstein condition for base manifold if the horizontal and vertical distributions of the ambient manifold is Einstein.
- warped product,
- warped-twisted product,
- Riemannian submersion
Citation: Richa Agarwal, Fatemah Mofarreh, Sarvesh Kumar Yadav, Shahid Ali, Abdul Haseeb. On Riemannian warped-twisted product submersions[J]. AIMS Mathematics, 2024, 9(2): 2925-2937. doi: 10.3934/math.2024144

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Abstract

In this paper, we introduce the concepts of Riemannian warped-twisted product submersions and examine their fundamental properties, including total geodesicity, total umbilicity and minimality. Additionally, we investigate the Ricci tensor of Riemannian warped-twisted product submersions, specifically about the horizontal and vertical distributions. Finally, we obtain Einstein condition for base manifold if the horizontal and vertical distributions of the ambient manifold is Einstein.

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