论文标题
关于某些Bianchi A型和相关的Kähler-Einstein指标的完整性
On the completeness of some Bianchi type A and related Kähler-Einstein metrics
论文作者
论文摘要
我们证明存在完全同一均匀性，一个三蛋白的Kähler-Einstein指标在欧几里得集团$ e（2）$的作用下。我们还展示了通过广义PDE给出的相关类型的Ricci FlatKähler指标的局部存在，并在轻度条件下确定它们是否完整。两种度量类型的常见框架是一个依赖框架的谎言支架关系和广义PDE的系统，该系统以$ 4 $ -MANIFOLDS的价格产生了一类Kähler-Einstein指标，其中包括所有对角线Bianchi A型指标。
We prove the existence of complete cohomogeneity one triaxial Kähler-Einstein metrics in dimension four under an action of the Euclidean group $E(2)$. We also demonstrate local existence of Ricci flat Kähler metrics of a related type that are given via generalized PDEs, and determine, under mild conditions, whether they are complete. The common framework for both metric types is a frame-dependent system of Lie bracket relations and generalized PDEs yielding a class of Kähler-Einstein metrics on $4$-manifolds which includes all diagonal Bianchi type A metrics.
