*-Ricci Solitons on Three-dimensional Normal Almost Contact Metric Manifolds

Abstract

The purpose of the paper is to study *-Ricci solitons and *-gradient Ricci solitons on three-dimensional normal almost contact metric manifolds. First, we prove that if a non-cosymplectic normal almost contact metric manifold with α, β = constant of dimension three admits a *-Ricci soliton, then the manifold is *-Ricci flat, provided β ≠ 0 and α ≠ ±β. Further, we prove that if a normal almost contact metric manifold with α, β = constant, of dimension three admits *-gradient Ricci soliton, then the manifold is *-Einstein, provided α2 − β2 ≠ 0.