2021/10/30 by Zhiming Feng, Feng, Zhiming
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2111.00294
openalex publication_date 2021/10/30 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28
The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally Kähler Einstein metrics on certain Hermitian holomorphic vector bundles and their subbundles over complete Kähler-Einstein manifolds. In special cases, we give the explicit expressions of of these metrics. These examples show that there is a compact Kähler manifold M and its subvariety N whose codimension is greater than 1 such that there is a complete conformally Kähler Einstein metric on M-N.