We review basic facts on the structure of nearly Kähler manifolds, focussing in particular on the six-dimensional case. A self-contained proof that nearly Kähler six-manifolds are Einstein is given by combining different known results. We finally rephrase the definition of nearly Kähler six-manifold in terms of a pair of partial differential equations.

中文翻译：

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近 Kähler 六流形上的爱因斯坦条件

我们回顾了几乎 Kähler 流形结构的基本事实，特别关注六维情况。通过结合不同的已知结果，给出了几乎 Kähler 六流形是爱因斯坦的独立证明。我们最终用一对偏微分方程重新表述了近 Kähler 六流形的定义。