Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

英文摘要：

Let $(X,J,g,ω)$ be a compact $2n$-dimensional almost-Kähler manifold. We prove primitive decompositions of $\partial$-, $\overline{\partial}$-harmonic forms on $X$ in bidegree $(1,1)$ and $(n-1,n-1)$ (such bidegrees appear to be optimal). We provide examples showing that in bidegree $(1,1)$ the $\partial$- and $\overline{\partial}$-decompositions differ.