Bott-Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds

Abstract

Let $(X,J,\omega )$ be a compact $2n$-dimensional almost Kähler manifold. We prove primitive decompositions for Bott-Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott-Chern, Aeppli, Dolbeault and $\partial$-harmonic forms on $(X,J,\omega )$ are related.