*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

Abstract

Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

Keywords

• almost kenmotsu manifold
• *-ricci soliton
• nullity distribution
• lie group
• primary 53d15
• secondary 53c25