η-Ricci solitons on 3-dimensional Kenmotsu manifolds

Abstract

The purpose of this paper is to study η-Ricci solitons on 3-dimensional Kenmotsu manifolds. First, we prove that an η-Ricci soliton on a 3-dimensional Kenmotsu manifold is an η-Einstein manifold. Besides these, we consider η-Ricci solitons on 3 -dimensional Kenmotsu manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Next, we study conformally at and φ-Ricci symmetric η-Ricci soliton on 3-dimensional Kenmotsu manifolds. Finally, we construct an example to prove the existence of η-Ricci soliton on 3-dimensional Kenmotsu manifold and verify some results.