On the spaces of (d + dc)-harmonic forms and (d + dλ)-harmonic forms on almost Hermitian manifolds and complex surfaces

In this paper, we study the spaces of (d + dc)-harmonic forms and of (d + dλ)-harmonic forms, a natural generalization of the spaces of Bott-Chern harmonic forms (respectively, symplectic harmonic forms) from complex (respectively, symplectic) manifolds to almost Hermitian manifolds.We apply the same techniques to compact complex surfaces, computing their Bott-Chern and Aeppli numbers and their spaces of (d + dλ)-harmonic forms. We give several applications to compact quotients of Lie groups by a lattice.