On 3-dimensional generalized (κ, μ)-contact metric manifolds

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ricci-symmetric, then it is a (κ, μ)-contact metric manifold. Further we investigated certain conditions under which a generalized (κ, μ)-contact metric manifold reduces to a (κ, μ)-contact metric manifold. Then we obtain several necessary and sufficient conditions for the Ricci tensor of a generalized (κ, μ)-contact metric manifold to be η-parallel. Finally, we studied Ricci-semisymmetric generalized (κ, μ)-contact metric manifolds and it is proved that such a manifold is either flat or a Sasakian manifold. M.S.C. 2000: 53C15, 53C05, 53C25.