2024
DOI: 10.33044/revuma.3557
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Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

Andrea Cattaneo,
Nicoletta Tardini,
Adriano Tomassini

Abstract: Let (X, J, g, ω) be a compact 2n-dimensional almost-Kähler manifold. We prove primitive decompositions of ∂-, ∂-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 ∂-and ∂-decompositions differ.

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