We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to the setting of almost Hermitian manifolds, allowing for new global results for such manifolds.

中文翻译：

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几乎埃尔米特身份

我们研究了Lefschetz算子与具有兼容度量的几乎复杂的流形上的外部微分之间的局部换向关系。我们获得的身份将本地Kähler身份的骨干推广到几乎Hermitian流形的设置，从而为此类流形提供了新的全局结果。