论文标题
广义的Kähler几乎是Abelian Lie团体
Generalized Kähler almost abelian Lie groups
论文作者
论文摘要
我们研究了几乎Abelian Lie群体的左旋广义Kähler结构，即具有编成一个Abelian正常亚组的可解决的谎言组。特别是，我们对六维的几乎Abelian Lie群体进行了分类，该群体承认了一个左右不变的复杂结构，并确定其中哪些具有左右不变的Hermitian结构，其基本的2Form为$ \ partial \ bar \ bar \ partial $ clucted。我们获得了六维广义的kähler几乎是阿贝利亚谎言组的分类，并确定了6维紧凑的几乎是Abelian Solvmanifolds，承认不变的广义Kähler结构。此外，我们证明了与植物泊松结构的存在以及多形流有关的一些结果。
We study left-invariant generalized Kähler structures on almost abelian Lie groups, i.e., on solvable Lie groups with a codimension-one abelian normal subgroup. In particular, we classify six-dimensional almost abelian Lie groups which admit a left-invariant complex structure and establish which of those have a left-invariant Hermitian structure whose fundamental 2-form is $\partial \bar \partial$-closed. We obtain a classification of six-dimensional generalized Kähler almost abelian Lie groups and determine the 6-dimensional compact almost abelian solvmanifolds admitting an invariant generalized Kähler structure. Moreover, we prove some results in relation to the existence of holomorphic Poisson structures and to the pluriclosed flow.
