Locally -symmetric normal almost contact metric manifolds of dimension 3

The object of the present work is to study a three-dimensional normal almost contact metric manifold which is locally ϕ -symmetric and whose Ricci tensor is η -parallel. First we obtain a necessary and sufficient condition for a three-dimensional normal almost contact metric manifold to be locally ϕ -symmetric. Next we prove that in such a manifold with α , β = constant if the Ricci tensor is η -parallel, then the manifold is locally ϕ -symmetric. Finally, an example of a three-dimensional locally ϕ -symmetric normal almost contact metric manifold is given.