Let \({\mathbb {F}}_{\Theta }=U/K_\Theta \) be a partial flag manifold, where \(K_\Theta \) is the centralizer of a torus in U. We study U-invariant almost Hermitian structures on \({\mathbb {F}}_{\Theta }\). The classification of these structures are naturally related with the system \(R_{\mathfrak {t}}\) of \({\mathfrak {t}}\)-roots associated to \({\mathbb {F}}_{\Theta }\). We introduced the notion of connectedness by triples with zero sum in a general subset of a vector space and proved that the set of \({\mathfrak {t}}\)-roots satisfies this property. Using this result, the invariant \({\mathcal {G}}_1\) structures on \({\mathbb {F}}_{\Theta }\) are completely classified.

令\（{\ mathbb {F}} _ {\ Theta} = U / K_ \ Theta \）为部分标志流形，其中\（K_ \ Theta \）是U中圆环的中心。我们研究\（{\ mathbb {F}} _ {\ Theta} \）上的U不变几乎Hermitian结构。这些结构的分类是天然与系统相关\（R _ {\ mathfrak {吨}} \）的\（{\ mathfrak {吨}} \） -roots关联到\（{\ mathbb {F}} _ { \ Theta} \）。我们在向量空间的一般子集中引入了具有零和的三元组的连通性概念，并证明了\（{\ mathfrak {t}} \）根的集合满足此属性。利用这个结果，不变式\（{\ mathbb {F}} _ {\ Theta} \）上的\（{\ mathcal {G}} _ 1 \）结构已完全分类。