论文标题
超复杂几乎是阿贝利安溶剂
Hypercomplex almost abelian solvmanifolds
论文作者
论文摘要
我们给出了几乎载有左不变超复合结构的几乎Abelian Lie组的表征，我们表明相应的Obata连接始终是平坦的。我们确定此类谎言何时允许HKT指标并研究相应的bismut连接。我们在维度8中获得了几乎是Abelian Lie组的分类，并确定哪些允许晶格。我们表明，相应的8维溶液溶液是Nilmanifolds或接收平坦的Hyper-Kähler指标。此外，我们证明任何8维紧凑的扁平高kähler歧管都是配备不变的超喀勒结构的溶剂。我们还在更高的维度中构建了几乎构建Abelian超复合Nilmanifolds和Solvmanifolds。
We give a characterization of almost abelian Lie groups carrying left invariant hypercomplex structures and we show that the corresponding Obata connection is always flat. We determine when such Lie groups admit HKT metrics and study the corresponding Bismut connection. We obtain the classification of hypercomplex almost abelian Lie groups in dimension 8 and determine which ones admit lattices. We show that the corresponding 8-dimensional solvmanifolds are nilmanifolds or admit a flat hyper-Kähler metric. Furthermore, we prove that any 8-dimensional compact flat hyper-Kähler manifold is a solvmanifold equipped with an invariant hyper-Kähler structure. We also construct almost abelian hypercomplex nilmanifolds and solvmanifolds in higher dimensions.
