Almost-complex invariants of families of six-dimensional solvmanifolds

Abstract

Abstract We compute almost-complex invariants h ∂ ¯ p , o h_{\bar \partial }^{p,o} , h D o l p , o h_{Dol}^{p,o} and almost-Hermitian invariants h δ ¯ p , o h_{\bar \delta }^{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 h ∂ ¯ p , q h_{\bar \partial }^{p,q} .