Locally Removable Singularities for K\"{a}hler Metrics with Constant Holomorphic Sectional Curvature

Si-en Gong; Hongyi Liu; Bin Xu

Locally Removable Singularities for K\"{a}hler Metrics with Constant Holomorphic Sectional Curvature

Differential Geometry 2019-09-05 v5 Complex Variables

Authors: Si-en Gong , Hongyi Liu , Bin Xu

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 K\"{a}hler metric on $B^{n}\setminus K$ with constant holomorphic sectional curvature uniquely extends to $B^{n}$ .

Keywords

kähler metric constant holomorphic sectional curvature removable singularities developing maps complex ball compact subset

Cite

@article{arxiv.1812.11719,
  title  = {Locally Removable Singularities for K\"{a}hler Metrics with Constant Holomorphic Sectional Curvature},
  author = {Si-en Gong and Hongyi Liu and Bin Xu},
  journal= {arXiv preprint arXiv:1812.11719},
  year   = {2019}
}

Comments

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

Locally Removable Singularities for K\"{a}hler Metrics with Constant Holomorphic Sectional Curvature

Abstract

Keywords

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