Abstract

A contact metric manifold whose characteristic vector field is a harmonic vector field is called an H-contact metric manifold. We introduce the notion of (κ,μ,ν)-contact metric manifolds in terms of a specific curvature condition. Then, we prove that a contact metric 3-manifold M is an H-contact metric manifold if and only if it is a (κ,μ,ν)-contact metric manifold on an everywhere open and dense subset of M. Also, we prove that, for dimensions greater than three, such manifolds are reduced to (κ,μ)-contact metric manifolds whereas, in three dimensions, (κ,μ,ν)-contact metric manifolds exist.

Keywords

contact metric manifolds, harmonic characteristic vector fields, H-contact manifolds, (κ, µ, ν)-contact metric manifolds

Mathematical Subject Classification

Primary: 53D10

Secondary: 53C25, 53C15

Authors