具有常全纯截曲率的Kähler度量的局部可去奇点

Si-en Gong; Hongyi Liu; Bin Xu

具有常全纯截曲率的Kähler度量的局部可去奇点

微分几何 2019-09-05 v5 复变函数

作者: Si-en Gong , Hongyi Liu , Bin Xu

摘要

设 $n\ge 2$ 为整数， $B^{n}\subset \mathbb{C}^{n}$ 为单位球。设 $K\subset B^{n}$ 为紧子集使得 $B^n\setminus K$ 连通，或 $K=\{z=(z_1,\cdots, z_n)|z_1=z_2=0\}\subset \mathbb{C}^{n}$ 。借助发展映射理论，我们证明 $B^{n}\setminus K$ 上具常全纯截曲率的Kähler度量可唯一延拓至 $B^{n}$ 。

关键词

Kähler度量常全纯截曲率可去奇点发展映射复球紧子集

引用

@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}
}

备注

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

具有常全纯截曲率的Kähler度量的局部可去奇点

摘要

关键词

引用

备注

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