Some geometric properties of η− Ricci solitons and gradient Ricci solitons on (𝑙𝑐𝑠)𝑛−manifolds

Abstract

In the context of para-contact Hausdorff geometry η−Ricci solitons and gradient Ricci solitons are considered on manifolds. We establish that on an (LCS)_ð‘›âˆ’manifold (M, Ï•, Î¾, Î·, g), the existence of an η−Ricci soliton implies that (M, g) is quasi-Einstein. We find conditions for Ricci solitons on an (LCS)_ð‘›âˆ’manifold (M, Ï•, Î¾, Î·, g) to be shrinking, steady and expanding. At the end we show examples of such manifolds with η−Ricci solitons.