Lie groups as 3-dimensional almost contact B-metric manifolds

TL;DR

This paper explores 3-dimensional Lie groups equipped with almost contact B-metric structures, establishing their existence, geometric properties, and providing examples to support the theoretical findings.

Contribution

It introduces the classification and geometric analysis of almost contact B-metric structures on 3D Lie groups, including explicit examples.

Findings

Existence of almost contact B-metric structures on all basic classes

Characterization of geometric properties of these structures

Explicit example supporting the theoretical results

Abstract

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results.