We prove that among all compact homogeneous spaces for an effective transitive action of a Lie group whose Levi subgroup has no compact simple factors, the seven-dimensional flat torus is the only one that admits an invariant torsion-free $\text{G}_{2(2)}$-structure.

中文翻译：

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紧凑的同质-歧管

我们证明，在李群没有紧单因子的李群的有效传递作用的所有紧齐次空间中，七维平面环面是唯一允许不变无扭的空间$\文本{G}_{2(2)}$-结构体。