Geometric characteristics and properties of a three-parametric family of Lie groups with almost contact B-metric structure of the smallest dimension

Abstract

Almost contact [Formula: see text]-metric manifolds of the lowest dimension 3 are constructed by a three-parametric family of Lie groups. Our aim is to determine the class of considered manifolds in a classification of almost contact [Formula: see text]-metric manifolds and their most important geometric characteristics and properties. Also, the type of the constructed Lie algebras is established in the Bianchi classification.