论文标题
韦尔因斯坦结构在保形溶剂上
Weyl-Einstein structures on conformal solvmanifolds
论文作者
论文摘要
保形的谎言组是一个保形歧管$（m，c）$，因此$ m $具有谎言组结构，而$ c $是$ m $上的剩余不变的度量$ g $定义的保形结构。我们研究Weyl-Einstein结构，这些结构及其紧凑型商组。在紧凑型情况下，我们表明每个带有韦尔因斯坦结构的共形溶剂溶液都是爱因斯坦。我们还表明，在非亚洲nilpotent的保形中没有剩余的Weyl-Einstein结构，并且在几乎亚洲的情况下，在可溶解的谎言组上对它们进行了分类。此外，我们确定了剩下的左右不变的Weyl-Einstein结构的简单连接的可解决的尺寸的左相连接的谎言基团的左右不变指标的精确列表（最多可达的）。
A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie group structure and $c$ is the conformal structure defined by a left-invariant metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie groups and on their compact quotients. In the compact case, we show that every conformal solvmanifold carrying a Weyl-Einstein structure is Einstein. We also show that there are no left-invariant Weyl-Einstein structures on non-abelian nilpotent conformal Lie groups, and classify them on conformal solvable Lie groups in the almost abelian case. Furthermore, we determine the precise list (up to automorphisms) of left-invariant metrics on simply connected solvable Lie groups of dimension 3 carrying left-invariant Weyl-Einstein structures.
