On some Lie groups as 5-dimensional almost contact B-metric manifolds with three natural connections

TL;DR

This paper investigates three natural linear connections on 5-dimensional Lie groups viewed as almost contact B-metric manifolds, focusing on their torsion properties and geometric structures.

Contribution

It introduces and analyzes three specific natural connections on 5D Lie groups with almost contact B-metric structures, highlighting their torsion conditions and geometric implications.

Findings

Characterization of three natural connections preserving the structure tensors

Analysis of torsion conditions for these connections

Application to a family of 5-dimensional Lie groups

Abstract

Almost contact manifolds with B-metric are considered. There are studied three natural connections (i.e. linear connections preserving the structure tensors) determined by conditions for their torsions. These connections are investigated on a family of Lie groups considered as 5-dimensional almost contact B-metric manifolds.