We look at methods to select triples $(M,\omega,J)$ consisting of a symplectic manifold $(M,\omega)$ endowed with compatible positive almost complex structure $J$, in terms the Nijenhuis tensor $N^J$ associated $J$. study particular image distribution $\Image N^J$.

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 fl...