Hermitian geometry of Lie algebras with abelian ideals of codimension 2 (Q6115065)

The authors show the usefulness of complex coordinates in the study of Hermitian structures, using as an illustrative example almost abelian Lie algebras. Then they consider Hermitian structures on Lie algebras which contain an abelian ideal of codimension two. In this case, properties of the Chern curvature are given. The main result gives a description of all Bismut torsion-parallel metrics on these Lie algebras.