ɳ-Ricci solitons in 3-dimensional normal almost contact metric manifolds

Abstract

The object of the present paper is to study the normal almost contact metric manifolds admitting the ɳ-Ricci Solitons. It is shown that a symmetric second-order covariant tensor in a normal almost contact metric manifold is a constant multiple of the metric tensor. Also an example of ɳ-Ricci soliton in 3-dimensional normal almost contacts metric manifolds is provided in the region where normal almost contact metric manifolds expand. Also, we obtain the ɳ-Ricci soliton in quasi Sasakian manifolds which satisfies cyclic parallel Ricci tensor, then the manifold is of constant curvature. Finally, we show the existence of such a manifold by an example.