Some Results on Normal Almost Contact Metric Manifolds of Dimension Three

The object of the present paper is to study a three dimensional normal almost contact metric manifold. First we study three dimensional normal almost contact metric manifolds with Q phi = phi Q and prove some equivalent conditions. Beside this locally phi-Ricci symmetry is studied here. Among others we prove that the xi-sectional curvature of this manifold is constant. All the above results are verified by non-trivial examples. Finally we study isometric immersion of a three dimensional normal almost contact metric manifold in a four dimensional Riemannian manifold of constant curvature 1.