Lie groups as 3-dimensional almost contact B-metric manifolds in the main vertical classes

Abstract

Almost contact B-metric manifolds of dimension 3 are constructed by a two-parametric family of Lie groups. The class of these manifolds in a known classification of almost contact B-metric manifolds is determined as the direct sum of the main vertical classes. The type of the corresponding Lie algebras in the Bianchi classification is given. Some geometric characteristics and properties of the considered manifolds are obtained.

6 pages

References in corpus (3)

• Lie groups as 3-dimensional almost contact B-metric manifolds
• On the structure tensors of almost contact B-metric manifolds
• Almost contact B-metric structures and the Bianchi classification of the three-dimensional Lie algebras