In this note, we show that for a closed almost-Kähler manifold (X,J) with the almost complex structure J satisfies dimker PJ = b2 − 1 the space of de Rham harmonic forms is contained in the space of symplectic-Bott–Chern harmonic forms. In particular, suppose that X is four-dimensional, if the self-dual Betti number b2+ = 1, then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott–Chern harmonic forms.

中文翻译：

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关于闭辛流形的第二非HLC度

在这篇笔记中，我们展示了对于一个封闭的几乎 Kähler 流形(X,Ĵ)具有几乎复杂的结构Ĵ满足暗淡克尔 磷Ĵ = b2 - 1de Rham 调和形式的空间包含在辛-Bott-Chern 调和形式的空间中。特别是，假设X是四维的，如果自对偶贝蒂数b2+ = 1，然后我们证明第二个非 HLC 度测量了 de Rham 和辛-Bott-Chern 谐波形式之间的差距。