Hermitian Structures on Lie Groups with Two-dimensional Commutator Subgroups

TL;DR

This paper classifies Hermitian structures on Lie groups with two-dimensional commutator subgroups, focusing on Kahler and Bismut connections, and provides explicit examples of various Kahler with torsion structures.

Contribution

It offers an explicit classification of Hermitian and Kahler structures on specific Lie groups, including Bismut connection computations and examples of torsion structures.

Findings

Classification of Hermitian structures into Type I and II

Identification of Kahler structures within these types

Examples of Kahler and strong/weak Kahler with torsion structures

Abstract

This article studies left-invariant Hermitian structures on Lie groups with two-dimensional commutator subgroups. We provide an explicit classification for two specific types of such structures, which we designate as Type I and Type II. Furthermore, we classify the Kahler structures within these two types and compute their associated Bismut connections. Finally, we present examples of Kahler and strong (respectively, weak) Kahler with torsion structures.