Almost-complex invariants of families of six-dimensional solvmanifolds

We compute almost-complex invariants hδ¯p,o, hDolp,o and almost-Hermitian invariants hδ¯p,o on families of almost-Kähler and almost-Hermitian 6-dimensional solvmanifolds. Finally, as a consequence of almost-Kähler identities we provide an obstruction to the existence of a compatible symplectic structure on a given compact almost-complex manifold. Notice that, when (X, J, g, ω) is a compact almost Hermitian manifold of real dimension greater than four, not much is known concerning the numbers hδ¯p,q.