Riemann solitons on Egorov and Cahen-Wallach symmetric spaces

Shahroud Azami; Rawan Bossly; Abdul Haseeb; Shahroud Azami; Rawan Bossly; Abdul Haseeb

doi:10.3934/math.2025087

AIMS Mathematics

2025, Volume 10, Issue 1: 1882-1899. doi: 10.3934/math.2025087

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Riemann solitons on Egorov and Cahen-Wallach symmetric spaces

1.
Department of pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
2.
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia

Received: 16 November 2024 Revised: 29 December 2024 Accepted: 22 January 2025 Published: 05 February 2025
MSC : 53C21, 53C25, 53E20

In this paper, we consider Egorov and Cahen-Wallach symmetric spaces and study the Riemann solitons on these spaces. We prove that Egorov and Cahen-Wallach symmetric spaces admit the Riemann solitons. Also, we classify the Riemann solitons on these spaces and show that the potential vector fields of the Riemann solitons are Killing, Ricci collineation, and Ricci bi-conformal vector fields.
- conformal vector fields,
- Walker manifolds,
- Riemannian metrics
Citation: Shahroud Azami, Rawan Bossly, Abdul Haseeb. Riemann solitons on Egorov and Cahen-Wallach symmetric spaces[J]. AIMS Mathematics, 2025, 10(1): 1882-1899. doi: 10.3934/math.2025087

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Abstract

In this paper, we consider Egorov and Cahen-Wallach symmetric spaces and study the Riemann solitons on these spaces. We prove that Egorov and Cahen-Wallach symmetric spaces admit the Riemann solitons. Also, we classify the Riemann solitons on these spaces and show that the potential vector fields of the Riemann solitons are Killing, Ricci collineation, and Ricci bi-conformal vector fields.

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