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Group manifolds and homogeneous spaces with HKT geometry: The role of automorphisms
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-05-14 , DOI: 10.1016/j.nuclphysb.2020.115052
A.V. Smilga

We present a new simple proof of the fact that certain group manifolds as well as certain homogeneous spaces G/H of dimension 4n admit a triple of integrable complex structures that satisfy the quaternionic algebra and are covariantly constant with respect to the same torsionful Bismut connection, i.e. exhibit the HKT geometry. The key observation is that different complex structures are interrelated by automorphisms of the Lie algebra. To construct the quaternion triples, one only needs to construct the proper automorphisms, which is a more simple problem.



中文翻译:

具有HKT几何的群流形和齐次空间:自同构的作用

我们提出了一个新的简单证明,即某些群流形以及某些齐次空间 G/H尺寸4 n的平方允许三元可积复杂结构,它们满足四元数代数并且相对于相同的扭转Bismut连接是协变常数,即表现出HKT几何形状。关键的观察是,李复数的自同构使不同的复杂结构相互关联。要构建四元数三元组,只需构建适当的自同构,这是一个更简单的问题。

更新日期:2020-06-18
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