The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2021-01-20 , DOI: 10.1007/s12220-020-00597-7 Gideon Maschler , Robert Ream
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.
中文翻译:
关于一些Bianchi A型和相关Kähler-Einstein度量的完备性
我们证明了在欧几里得群E(2)的作用下,在第4维上存在完全同质的三轴Kähler-Einstein度量。我们还证明了通过广义PDE给出的相关类型的Ricci FlatKähler度量的局部存在,并在温和条件下确定它们是否完整。两种度量标准类型的通用框架是一个与框架相关的李括号关系系统和广义PDE,它们在4个流形上产生一类Kähler-Einstein度量标准,其中包括所有对角Bianchi A型度量标准。