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

Abstract

Let $(X,J,g,\omega )$ 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.

Final version to appear on "Revista de la Unión Matemática Argentina"

Cited by in corpus (1)

• On the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds