Almost Kenmotsu 3-h-metric as a cotton soliton

Abstract

Purpose – Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds. Design/methodology/approach – The authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations. Findings – First the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors 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. Originality/value – The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.

Keywords

• Almost Kenmotsu manifolds
• Cotton solitons
• Non-unimodular lie group
• Product space