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Mathematics > Differential Geometry

arXiv:1812.11719 (math)
[Submitted on 31 Dec 2018 (v1), last revised 4 Sep 2019 (this version, v5)]

Title:Locally Removable Singularities for Kähler Metrics with Constant Holomorphic Sectional Curvature

Authors:Si-en Gong, Hongyi Liu, Bin Xu
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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 $B^{n}$.
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
Subjects: Differential Geometry (math.DG); Complex Variables (math.CV)
Cite as: arXiv:1812.11719 [math.DG]
  (or arXiv:1812.11719v5 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1812.11719

Submission history

From: Si-En Gong [view email]
[v1] Mon, 31 Dec 2018 08:17:27 UTC (32 KB)
[v2] Thu, 6 Jun 2019 05:08:40 UTC (33 KB)
[v3] Mon, 15 Jul 2019 09:45:38 UTC (34 KB)
[v4] Sat, 3 Aug 2019 14:11:12 UTC (34 KB)
[v5] Wed, 4 Sep 2019 13:58:44 UTC (17 KB)
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