$\eta$-Ricci Solitons on Kenmotsu 3-Manifolds

TL;DR

This paper investigates $\eta$-Ricci solitons on Kenmotsu 3-manifolds, exploring special Ricci tensor conditions, symmetry properties, and curvature conditions, and provides an example demonstrating the existence of such solitons.

Contribution

It introduces new results on $\eta$-Ricci solitons in Kenmotsu 3-manifolds, including conditions with Codazzi and cyclic parallel Ricci tensors, and constructs an explicit example.

Findings

Existence of proper $\eta$-Ricci solitons on Kenmotsu 3-manifolds

Characterization under Codazzi and cyclic Ricci tensor conditions

Curvature condition $R.R=Q(S,R)$ satisfied in some cases

Abstract

In the present paper we study $\eta$-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider $\eta$-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study $\phi$-Ricci symmetric $\eta$-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 $\eta$-Ricci soliton on a Kenmotsu 3-manifold.