Almost contact B-metric manifolds with curvature tensors of Kähler type

Abstract

On 5-dimensional almost contact B-metric manifolds, the form of any Kähler-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 Kähler-type tensor for the canonical connection on the manifolds from the main classes with closed 1-forms.

12 pages

References in corpus (2)

• A classification of the torsion tensors on almost contact manifolds with B-metric
• A natural connection on some classes of almost contact manifolds with B-metric

Cited by in corpus (1)

• Invariant tensors related with natural connections for a class Riemannian product manifolds