In this paper, we study ∗-Conformal $η$ -Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal $η$ -Ricci soliton. We obtain some significant results on ∗-Conformal $η$ -Ricci soliton in Sasakian manifolds satisfying $R (ξ, X) \cdot S = 0$ , $S (ξ, X) \cdot R = 0$ , $\bar{P} (ξ, X) \cdot S$ $= 0$ , where $\bar{P}$ is Pseudo-projective curvature tensor. The conditions for ∗-Conformal $η$ -Ricci soliton on $ϕ$ -conharmonically flat and $ϕ$ -projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal $η$ -Ricci soliton.

Communicated by W. C. Cheung

Keywords:

AMSC: 53A30, 53C15, 53C25, 53D15

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