$\hat{I}\cdot$-Ricci Solitons on Kenmotsu 3-Manifolds

Abstract

In the present paper we study $\hat{I}\cdot$-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider $\hat{I}\cdot$-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study $\ddot{I}•$-Ricci symmetric $\hat{I}\cdot$-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition $R.R=Q(S,R)$ is considered. Finally, an example is constructed to prove the existence of a proper $\hat{I}\cdot$-Ricci soliton on a Kenmotsu 3-manifold.