2020/07/13 by Gideon Maschler, Maschler, Gideon, Robert K. Ream +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.2007.06471
minor changes
openalex publication_date 2020/07/13 · arxiv created 2021/01/05 · arxiv updated 2021/01/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.