Locally Removable Singularities for Kähler Metrics with Constant Holomorphic Sectional Curvature

Abstract

Let $n\ge 2$ be an integer, and $B^n\subset {\mathbb{C}}^n$ the unit ball. Let $K\subset B^n$ be a compact subset such that $B^n\setminus K$ is connected, or $K=\{z=(z_1,\cdots ,z_n)|z_1=z_2=0\}\subset {\mathbb{C}}^n$. By the theory of developing maps, we prove that a Kähler metric on $B^n\setminus K$ with constant holomorphic sectional curvature uniquely extends to $B^n$.

13 pages, 2 figures. We made the following revisements: 1. We added a new condition in Theorem 1.1 that $B^n\setminus K$ is connected, which is necessary for the truth of the theorem. 2. We added Remark 1.4, which says that there do exist isolated singularities for Riemannian metrics of constant sectional curvature in real dimension three or more