Hermitian structures on a class of almost nilpotent solvmanifolds

In this paper we investigate the existence of invariant SKT, balanced and generalized Kähler structures on compact quotients Γ﹨G, where G is an almost nilpotent Lie group whose nilradical has one-dimensional commutator Γ a lattice G. We first obtain characterization Hermitian algebras g n classification result in real dimension six. Then, study ones admitting SKT examine behaviour such under flows. particular, construct new examples manifolds. Finally, prove some non-existence results for higher non-split (i.e., that associated complex do not commute) abelian algebras. This leads to (non-Kähler) manifolds structures.