论文标题
在两步可解决的谎言组上平衡和SKT指标的兼容性
Compatibility of balanced and SKT metrics on two-step solvable Lie groups
论文作者
论文摘要
Fino和Vezzoni已经猜想，一个紧凑的复合歧管，同时承认兼容的SKT和兼容的平衡度量也承认了兼容的Kähler指标。使用以前工作的两步可溶剂SKT的剪切构造和分类结果，我们证明了这种猜想的构想，用于具有不变的复杂结构，该结构是（a）的（a）pure-type of pure，或（a）的维度六。相比之下，我们提供了两个反示例，以在同质不变的环境中自然概括这种猜想。作为工作的一部分，我们在两步可溶的谎言组上获得了不变的SKT，平衡和Kähler结构的进一步分类结果。特别是，我们在第六位的两步溶解谎言基团上对剩余的SKT结构进行了完整分类。
It has been conjectured by Fino and Vezzoni that a compact complex manifold admitting both a compatible SKT and a compatible balanced metric also admits a compatible Kähler metric. Using the shear construction and classification results for two-step solvable SKT Lie algebras from our previous work, we prove this conjecture for compact two-step solvmanifolds endowed with an invariant complex structure which is either (a) of pure type or (b) of dimension six. In contrast, we provide two counterexamples for a natural generalisation of this conjecture in the homogeneous invariant setting. As part of the work, we obtain further classification results for invariant SKT, balanced and Kähler structures on two-step solvable Lie groups. In particular, we give the full classification of left-invariant SKT structures on two-step solvable Lie groups in dimension six.
