We study conformal Killing forms on compact 6-dimensional nearly Kähler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of dω and its Hodge dual $⁎d\omega$, where ω is the fundamental 2-form of the nearly Kähler structure. The proof is based on a fundamental integrability condition for conformal Killing forms. We have partial results in the case of conformal Killing 2-forms. In particular we show the non-existence of J-anti-invariant Killing 2-forms.

中文翻译：

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几乎Kähler流形上的保形杀伤形式

我们研究紧凑的6维近Kähler流形上的共形Killing形式。我们的主要结果涉及3级形式。在这里，我们给出一个分类，表明所有保形的Killing 3型都是dω及其Hodge对偶的线性组合$⁎d\omega$，其中ω是几乎Kähler结构的基本2形式。证明是基于保形Killing形式的基本可积性条件。对于保形Killing 2形式，我们有部分结果。特别地，我们显示了J反抗杀死2形式的不存在。