Riemann solitons on Egorov and Cahen-Wallach symmetric spaces

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.

Keywords

• conformal vector fields
• walker manifolds
• riemannian metrics