Balanced Hermitian structures on almost abelian Lie algebras

We study balanced Hermitian structures on almost abelian Lie algebras, i.e. algebras with a codimension-one ideal. In particular, we classify six-dimensional which carry structure. It has been conjectured in [1] that compact complex manifold admitting both metric and an SKT necessarily Kähler metric: prove this conjecture for solvmanifolds left-invariant structures. Moreover, investigate the behaviour of flow metrics introduced [2] anomaly [3] groups. show preserves condition locally conformally are fixed points.