We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced SU(n)-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull–Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler \(\text {SU}(3)\)-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.

中文翻译：

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关于同质性的六流形的平衡度量的存在性一

我们考虑具有全纯平凡规范丛的复杂流形上的平衡度量，最常称为平衡 SU(n) 结构。这种结构对 Hermitian 几何和弦理论都很感兴趣，因为它们为 Hull-Strominger 系统提供了理想的设置。在本文中，我们为平衡的非 Kähler \(\text {SU}(3)\) -结构提供了不存在结果，这些结构在简单连接的六流形上的同质性单作用下是不变的。