Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive decompositions of Dolbeault harmonic forms on compact
  almost-K\"ahler manifolds   Let $(X,J,g,\omega)$ be a compact $2n$-dimensional almost-K\"ahler 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.

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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas