We study multi-moment maps induced by a two-torus action on the four homogeneous nearly Kahler six-manifolds. Their explicit expression and stationary orbits are derived. The configuration of fixed-points and one-dimensional orbits is worked out for generic six-manifolds equipped with an $\mathrm{SU}(3)$-structure admitting a two-torus symmetry. Projecting the subspaces obtained to the orbit space yields a trivalent graph. We illustrate this result concretely on the homogeneous nearly Kahler examples.

中文翻译：

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近 Kähler 六流形上的多矩图

我们研究了由四个均质近乎 Kahler 六流形上的两个环面作用引起的多矩图。推导出它们的显式表达式和静止轨道。不动点和一维轨道的配置是为通用六流形制定的，该流形配备了 $\mathrm{SU}(3)$-结构，允许两个圆环对称。将获得的子空间投影到轨道空间产生一个三价图。我们在齐次的近 Kahler 例子上具体说明了这个结果。