The (κ, μ, ν)-contact metric manifolds and their classification in the 3-dimensional case

A Class of 3-dimensional Contact Metric Manifolds

“…In section 3 we give some properties of contact metric 3-dimensional manifold. In section 4 we generalize the corollaries of [13] and [14]. Finally we gave two examples which satisfiy the conditions of this manifold.…”

“…Moreover, the authors locally classified three dimensional (κ, µ, υ)-contact metric manifolds which satisfy the condition ∇ ξ τ = 2aτ φ in [14]. They gave the following theorem.…”

“…In [13] locally classified the 3-dimensional generalized (κ, µ)-contact metric manifolds satisfied the condition gradκ =constant( = 0) . In [14] locally classified the 3-dimensional (κ, µ, v)-contact metric manifolds which satisfy the condition ∇ ξ τ = 2aτ φ, where a is a smooth function. In this paper we want to generalize the corollaries of [13] and [14] .…”

“…In [14] locally classified the 3-dimensional (κ, µ, v)-contact metric manifolds which satisfy the condition ∇ ξ τ = 2aτ φ, where a is a smooth function. In this paper we want to generalize the corollaries of [13] and [14] . The paper is organized in the following way.…”

A class of 3-dimensional almost cosymplectic manifolds

“…This work was inspired by [14] and [13]. We carry on those studies to the 3 -dimensional almost cosymplectic manifolds in this paper.…”