Conformal $$\eta $$-Einstein Soliton on $$(LCS)_{n}$$-Manifold

The object of the present paper is to study conformal $$\eta $$ -Einstein soliton in the framework of $$(LCS)_{n}$$ -manifold. First we establish the existence of conformal $$\eta $$ -Einstein soliton on $$(LCS)_{n}$$ -manifold. Then we obtain some results on $$(LCS)_{n}$$ -manifold admitting conformal $$\eta $$ -Einstein soliton where the Ricci tensor is cyclic parallel and Codazzi type. We have also considered the soliton where the manifold is Ricci symmetric.