On the spaces of $(d+d^c)$-harmonic forms and $(d+d^{\Lambda })$-harmonic forms on almost Hermitian manifolds and complex surfaces

Abstract

In this paper, we study the spaces of $(d+d^c)$-harmonic forms and of $(d+d^{\Lambda })$-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 $(d+d^{\Lambda })$-harmonic forms. We give several applications to compact quotients of Lie groups by a lattice.