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

TL;DR

This paper constructs 3-dimensional almost contact B-metric manifolds using Lie groups, classifies them within known categories, and analyzes their geometric properties and Lie algebra types.

Contribution

It introduces a two-parameter family of Lie group-based manifolds and classifies them as a sum of main vertical classes, detailing their algebraic and geometric features.

Findings

Manifolds form a two-parameter family of Lie groups.

Classified as direct sum of main vertical classes.

Identified Lie algebra types in Bianchi classification.

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.