论文标题
Vaisman流形和横向的Kähler-Einstein指标
Vaisman manifolds and transversally Kähler-Einstein metrics
论文作者
论文摘要
我们在封闭的Vaisman歧管的规范叶上使用横向Kähler-Ricci流，以将Vaisman指标变形为具有横向Kähler-Einstein结构的另一个Vaisman度量。我们还研究了这种歧管的主要特征。除其他结果外，使用来自抛物线方程理论的技术，我们还可以直接证明横向{\ k} -ricci流在Vaisman歧管上流动的解决方案，并在特定环境中恢复了Bedulli，他和Vezzoni [J.] [J.地理。肛门。 28，697--725（2018）]，但不采用Molino结构定理。此外，我们在Vaisman歧管的环境中研究了爱因斯坦 - 韦尔的结构，并找到了它们与准元素指标的关系。还提供了一些示例来说明主要结果。
We use the transverse Kähler-Ricci flow on the canonical foliation of a closed Vaisman manifold to deform the Vaisman metric into another Vaisman metric with a transverse Kähler-Einstein structure. We also study the main features of such a manifold. Among other results, using techniques from the theory of parabolic equations, we obtain a direct proof for the short time existence of the solution for transverse {\K}-Ricci flow on Vaisman manifolds, recovering in a particular setting a result of Bedulli, He and Vezzoni [J. Geom. Anal. 28, 697--725 (2018)], but without employing the Molino structure theorem. Moreover, we investigate Einstein-Weyl structures in the setting of Vaisman manifolds and find their relationship with quasi-Einstein metrics. Some examples are also provided to illustrate the main results.
