Contact 3-manifolds and ＊-Ricci soliton

Abstract

Let (M,φ,ζ,η,g) be a three-dimensional Kenmotsu manifold. In this paper, we prove that the triple (g,V,λ) on M is a ＊-Ricci soliton if and only if M is locally isometric to the hyperbolic 3-space H³(-1) and λ=0. Moreover, if g is a gradient ＊-Ricci soliton, then the potential vector field coincides with the Reeb vector field. We also show that the metric of a coKähler 3-manifold is a ＊-Ricci soliton if and only if it is a Ricci soliton.