Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds

The object of the present paper is to study a 3-dimensional normal almost contact metric manifold admitting Ricci solitons and gradient Ricci solitons. At first we give an example of a 3-dimensional normal almost contact metric manifold with alpha,beta = constant. We prove that a 3-dimensional normal almost contact metric manifold admitting a Ricci soliton with a potential vector field V collinear with the characteristic vector field xi, is eta-Einstein provided alpha,beta = constant. Also we show that an eta-Einstein 3-dimensional normal almost contact metric manifold with alpha,beta = constant and V = xi admits a Ricci soliton. Finally we prove that if in a 3-dimensional normal almost contact metric manifold with constant scalar curvature, g is a gradient Ricci soliton, then the manifold is either alpha-Kenmotsu or an Einstein manifold provided alpha,beta = constant.