Hermitian Structures on Lie Groups with Two-dimensional Commutator Subgroups

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.