On transversally symmetric pseudo-Einstein and Fefferman–Einstein spaces
On transversally symmetric pseudo-Einstein and Fefferman–Einstein spaces
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关于横向对称伪爱因斯坦和费弗曼-爱因斯坦空间
DOI：
10.1007/s00209-007-0121-8
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发表时间：
2007
影响因子：
0.8
通讯作者：
Felipe Leitner
中科院分区：
文献类型：
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作者：
Felipe Leitner
我们描述并构造了无挠（即具有横对称性）的伪厄米特结构θ，其Webster-Ricci曲率张量是外微分θ的常数倍.我们称这些结构为TS-伪爱因斯坦，我们的第一个结果表明，所有这些结构都可以局部地从Kähler-Einstein度量导出。然后我们讨论了TS-伪爱因斯坦结构的相应的费曼度规。他们从来都不是爱因斯坦。然而，我们的第二个结果指出，他们总是局部共形爱因斯坦。
We describe and construct pseudo-Hermitian structuresθwithout torsion (i.e. with transverse symmetry) whose Webster–Ricci curvature tensor is a constant multiple of the exterior differentialdθ. We call these structures TS-pseudo-Einstein and our first result states that all these structures can locally be derived from Kähler–Einstein metrics. Then we discuss the corresponding Fefferman metrics of the TS-pseudo-Einstein structures. These are never Einstein. However, our second result states that they are locally always conformally Einstein.