论文标题
爱因斯坦Solvmanifolds上的伪-Kähler和Pseudo-Sasaki结构
Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds
论文作者
论文摘要
本文的目的是在可解决的谎言基团上构建左行不变的爱因斯坦伪里曼尼亚人的sasaki指标。 我们考虑$ \ Mathfrak Z $ - 标准的Sasaki可解决的lie代数$ 2N+3 $，它们与Pseudo-kählernilpotent lie代数为一对一，尺寸为$ 2N $，具有兼容的衍生品，从适当的意义上讲。我们表征了伪-Kähler结构和派生，从而引起了Sasaki-Einstein指标。 我们对$ \ Mathfrak z $ - 标准sasaki sasaki可解决的谎言lie代数$ \ leq 7 $，以及那些伪kähler降低的人是Abelian Lie Algebra。 我们获得的爱因斯坦指标是标准的，但不是伪iwasawa型。
The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one correspondence with pseudo-Kähler nilpotent Lie algebras of dimension $2n$ endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-Kähler structures and derivations giving rise to Sasaki-Einstein metrics. We classify $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $\leq 7$ and those whose pseudo-Kähler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type.
