Some results of η-Ricci solitons on (LCS)n-manifolds

Abstract

In this paper, we consider an η -Ricci soliton on the (LCS)n-manifolds (M, φ , ξ , η , g) satisfying certain curvature conditions likes: R(ξ , X) · S= 0 and W 2(ξ, X) · S=0. We show that on the (LCS)n-manifolds (M,φ ,ξ ,η ,g), the existence of η -Ricci soliton implies that (M, g) is a quasi-Einstein. Further, we discuss the existence of Ricci solitons with the potential vector field ξ. In the end, we construct the non-trivial examples of η -Ricci solitons on the (LCS)n-manifolds.

Keywords

• η -Ricci soliton; Quasi-Einstein
• η -Ricci soliton
• Quasi-Einstein
• (LCS)n-manifold
• Ricci tensors
• Curvature tensors