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A One-Dimensional Singular Non-CSC Extremal Kähler Metric can be Isometrically Imbedded into $${\mathbb {R}}^3$$ as a Weingarten Surface
Results in Mathematics ( IF 1.1 ) Pub Date : 2020-08-15 , DOI: 10.1007/s00025-020-01258-5
Chia-Kuei Peng , Yingyi Wu

In this paper, we get a one-parameter family of local isometric immersions from a compact Riemann surface with a singular non-CSC extremal Kahler metric to $${\mathbb {R}}^3$$ , each of whom is a Weingarten surface. In fact, we can get explicit expressions of the mean curvatures in the family by the Gauss curvature of the metric.

中文翻译:

一维奇异非 CSC 极值 Kähler 度量可以等距嵌入 $${\mathbb {R}}^3$$ 作为 Weingarten 曲面

在本文中,我们从具有奇异非 CSC 极值 Kahler 度量的紧凑黎曼曲面到 $${\mathbb {R}}^3$$ 获得了一个局部等距浸入的单参数族,其中每个都是 Weingarten表面。事实上,我们可以通过度量的高斯曲率得到族中平均曲率的显式表达。
更新日期:2020-08-15
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