On minimal immersions of a singular non-CSC extremal Kahler metric into 3-dimensional space forms

Wei Zhiqiang; Wu Yingyi

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On minimal immersions of a singular non-CSC extremal Kahler metric into 3-dimensional space forms

机译：将单一非 CSC 极值 Kahler 度量最小浸入 3 维空间形式

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On any compact Riemann surface there always exists a singular non-CSC (constant scalar curvature) extremal Kahler metric which is called a non-CSC HCMU (the Hessian of the Curvature of the Metric is Umbilical) metric. In this paper, by moving frames, we show that any non-CSC HCMU metric can not be minimally immersed into 3-dimensional real space forms even locally. In general, any non-CSC HCMU metric can not be isometrically immersed into 3-dimensional real space forms with constant mean curvature.

机译：在任何紧黎曼曲面上，始终存在一个奇异的非 CSC（恒定标量曲率）极值 Kahler 度量，称为非 CSC HCMU（度量曲率的 Hessian 是脐带）度量。在本文中，通过移动帧，我们证明了任何非CSC HCMU度量都不能最小地浸入三维真实空间形式中，即使是局部的。一般来说，任何非CSC HCMU度量都不能等距地浸入具有恒定平均曲率的三维真实空间形式中。

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《Geometriae Dedicata》 |2023年第2期|共11页
作者
Wei Zhiqiang; Wu Yingyi;
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作者单位

Henan Univ;

Univ Chinese Acad Sci;

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正文语种英语
中图分类几何、拓扑;
关键词
HCMU metric; Minimal immersion; Moving frames; HERMITIAN METRICS; CURVATURE; SURFACES; EXISTENCE;

机译：HCMU 指标;最低沉浸感;移动框架;赫米特指标;曲率;曲面;存在;

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1. Local Isometric Imbedding of a Compact Riemann Surface with a Singular Non-CSC Extremal Kahler Metric into 3-Dimension Space Forms [J] . Wei Zhiqiang, Wu Yingyi The Journal of geometric analysis . 2022,第1期

机译：Local Isometric Imbedding of a Compact Riemann Surface with a Singular Non-CSC Extremal Kahler Metric into 3-Dimension Space Forms
2. Geometry and topology of the space of Kahler metrics on singular varieties [J] . Di Nezza Eleonora, Guedj Vincent Compositio mathematica . 2018,第8期

机译：Geometry and topology of the space of Kahler metrics on singular varieties
3. Minimal isometric immersions of spherical space forms in spheres [J] . DennisDeTurck, WolfgangZiller commentarii mathematici helvetici . 2007,第1期

机译：Minimal isometric immersions of spherical space forms in spheres
4. Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence [O] . Cvetic, M., Gibbons, G. W., Lu, H., 2001

机译：Hyper-Kahler Calabi metrics，L ^ 2 Harmonic Forms，Resolved m2-branes，and ads_4 / CFT_3通信

On minimal immersions of a singular non-CSC extremal Kahler metric into 3-dimensional space forms

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