Cotton Solitons on Almost Kenmotsu 3-$h$-Manifolds

TL;DR

This paper studies Cotton solitons on almost Kenmotsu 3-h-manifolds, proving non-existence under certain conditions and characterizing steady solitons when the potential vector field is orthogonal to the Reeb vector field.

Contribution

It introduces new results on the existence and properties of Cotton solitons in almost Kenmotsu 3-h-manifolds, including non-existence and classification of steady solutions.

Findings

Non-existence of Cotton solitons with potential vector collinear to Reeb vector

Steady Cotton solitons with orthogonal potential vector are locally isometric to hyperbolic space times a line

Characterization of Cotton solitons when Reeb vector is an eigenvector of Ricci operator

Abstract

In this paper, we consider the notion of Cotton soliton within the framework of almost Kenmotsu 3-$h$-manifolds. First we consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next we assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-$h$-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to $\mathbb{H}^2(-4) \times \mathbb{R}$.