Almost contact B-metric manifolds with curvature tensors of K\"ahler type

Abstract

On 5-dimensional almost contact B-metric manifolds, the form of any K\"ahler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvatures of the K\"ahler-type tensor for the canonical connection on the manifolds from the main classes with closed 1-forms.