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

Abstract

Abstract:The object of the present paper is to obtain a necessary and sufficient condition for a 3 -dimensional generalized (κ, µ) -contact metric manifold to be locally ϕ-symmetric in the sense of Takahashi and the condition is verified by an example. Next we characterize a 3 -dimensional generalized (κ, µ) -contact metric manifold satisfying certain curvature conditions on the concircular curvature tensor. Finally, we construct an example of a generalized (κ, µ) -contact metric manifold to verify Theorem 1 of our paper.