Conformal η-Ricci solitons within the framework of indefinite Kenmotsu manifolds

The present paper is to deliberate the class of epsilon-Kenmotsu manifolds which admits conformal eta-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal eta-Ricci soliton of epsilon-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal eta-Ricci solitons on epsilon-Kenmotsu manifolds. Next, we consider gradient conformal eta-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal eta-Ricci soliton on eta-Kenmotsu manifold.

Automated summary

This paper discusses the class of epsilon-Kenmotsu manifolds that have conformal eta-Ricci solitons. It studies the special types of Ricci tensor associated with conformal eta-Ricci solitons on epsilon-Kenmotsu manifolds. Additionally, it investigates curvature conditions that allow for conformal eta-Ricci solitons on epsilon-Kenmotsu manifolds. Furthermore, the paper presents a characterization of the potential function for gradient conformal eta-Ricci solitons. Lastly, an illustrative example is provided to demonstrate the existence of conformal eta-Ricci solitons on eta-Kenmotsu manifolds.