论文标题
平衡的赫尔米尼人在几乎是阿贝利安谎言代数上的结构
Balanced Hermitian structures on almost abelian Lie algebras
论文作者
论文摘要
我们研究了几乎是阿贝利亚谎言代数的平衡遗产结构，即具有一个codimensionsimension-One Abelian理想的谎言代数。特别是，我们对带有平衡结构的六维几乎阿比亚利亚代数进行了分类。 A. Fino和L. vezzoni已经猜想了一个紧凑的复合歧管，既容纳平衡度量，又有SKT度量标准必须具有Kähler指标：我们证明了这种猜想是紧凑的几乎是Abelian Solvmanifolds，并具有剩余不变的复杂结构。此外，我们研究了L. Bedulli和L. vezzoni引入的平衡指标流的行为，以及几乎Abelian Lie组的D. H. Phong，S。Picard和X. Zhang的异常流动。特别是，我们表明异常流保持平衡状态，而局部合成的Kähler指标是固定点。
We study balanced Hermitian structures on almost abelian Lie algebras, i.e. on Lie algebras with a codimension-one abelian ideal. In particular, we classify six-dimensional almost abelian Lie algebras which carry a balanced structure. It has been conjectured by A. Fino and L. Vezzoni that a compact complex manifold admitting both a balanced metric and a SKT metric necessarily has a Kähler metric: we prove this conjecture for compact almost abelian solvmanifolds with left-invariant complex structures. Moreover, we investigate the behaviour of the flow of balanced metrics introduced by L. Bedulli and L. Vezzoni and of the anomaly flow by D. H. Phong, S. Picard and X. Zhang on almost abelian Lie groups. In particular, we show that the anomaly flow preserves the balanced condition and that locally conformally Kähler metrics are fixed points.
