Revista de la
Unión Matemática Argentina
Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds
Andrea Cattaneo, Nicoletta Tardini, and Adriano Tomassini

Volume 67, no. 1 (2024), pp. 301–316    

Published online: May 22, 2024

https://doi.org/10.33044/revuma.3557

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Abstract

Let $(X,J,g,\omega)$ be a compact $2n$-dimensional almost-Kähler manifold. We prove primitive decompositions of $\partial$-, $\bar\partial$-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 $\bar\partial$-decompositions differ.

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