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

TL;DR

This paper constructs three-dimensional almost contact B-metric manifolds using Lie groups, classifies their Lie algebras, and explores their geometric properties, providing insights into their structure and significance.

Contribution

It introduces a three-parameter family of Lie group-based manifolds and classifies their Lie algebras within the Bianchi scheme, highlighting their geometric features.

Findings

Identification of a specific class with geometric significance

Classification of Lie algebras in the Bianchi scheme

Description of geometric properties of the manifolds

Abstract

Three-dimensional almost contact B-metric manifolds are constructed by a three-parametric family of Lie groups. It is established the class of the investigated manifolds which has an important geometrical interpretation. It is determined also the type of the constructed Lie algebras in the Bianchi classification. There are given some geometric characteristics and properties of the considered manifolds.