在复二维仿射锥上的完备余齐性一Kähler度量

doi:10.13371/j.cnki.chin.q.j.m.2024.02.008

数学季刊 ›› 2024, Vol. 39 ›› Issue (2): 200-220.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.008

• • 上一篇

在复二维仿射锥上的完备余齐性一Kähler度量

关庄丹^1,2, 梁梦翔¹

1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

收稿日期:2023-07-14 出版日期:2024-06-30 发布日期:2024-06-30
通讯作者: LIANG Meng-xiang (2000-), male, native of Kaifeng, Henan, Ph.D student of Henan University. E-mail: liang mx@henu.edu.cn
作者简介:GUAN Daniel (1962-), male, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in complex geometry. LIANG Meng-xiang (2000-), male, native of Kaifeng, Henan, Ph.D student of Henan University.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 12171140).

Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br#

GUAN Daniel^1,2, LIANG Meng-xiang¹

1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

Received:2023-07-14 Online:2024-06-30 Published:2024-06-30
Contact: LIANG Meng-xiang (2000-), male, native of Kaifeng, Henan, Ph.D student of Henan University. E-mail: liang mx@henu.edu.cn
About author:GUAN Daniel (1962-), male, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in complex geometry. LIANG Meng-xiang (2000-), male, native of Kaifeng, Henan, Ph.D student of Henan University.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 12171140).

摘要/Abstract

摘要： In this paper, we revisit the K¨ahler structures on the affine quadrics M₁={z₁² +z₂² +z₃² = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen.

关键词: 1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China, 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

Abstract: In this paper, we revisit the K¨ahler structures on the affine quadrics M₁={z₁² +z₂² +z₃² = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen.

Key words: 1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China, 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

中图分类号:

关庄丹, 梁梦翔. 在复二维仿射锥上的完备余齐性一Kähler度量[J]. 数学季刊, 2024, 39(2): 200-220.

GUAN Daniel, LIANG Meng-xiang. Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br#[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 200-220.

[1]	辛欣, 谢博易, 刘科科. 基于半参数Copula学习的确定性独立筛选研究[J]. 数学季刊, 2024, 39(2): 144-160.
[2]	席维鸽, 许涛. 非正则赋权有向图 A_a谱半径的上界[J]. 数学季刊, 2024, 39(2): 161-170.
[3]	许云龙, 钟裕民. Bouw-M¨oler曲面的Minkowski常数[J]. 数学季刊, 2024, 39(2): 185-199.
[4]	江东月, 唐忠华, 房少梅. 具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破[J]. 数学季刊, 2024, 39(2): 111-127.
[5]	唐忠华, 房少梅. 带分数阶Robin边界条件的时间-空间分数阶扩散方程的有限差分方法[J]. 数学季刊, 2024, 39(1): 18-30.
[6]	洪勇, 赵茜. 两类加权空间间的积分算子与离散算子的有界性及算子范数估计[J]. 数学季刊, 2024, 39(1): 59-67.
[7]	王川, 乔炎. Korteweg-de Vries方程的Legendre时空谱配置方法[J]. 数学季刊, 2023, 38(4): 392-400.
[8]	许娜. 一类次线性基尔霍夫方程基态解的存在性[J]. 数学季刊, 2023, 38(4): 410-414.
[9]	杨亦松. 曲面上的曲率在理论物理中的一些应用[J]. 数学季刊, 2023, 38(3): 221-253.
[10]	徐晓濛. Stokes 现象与量子群的表示[J]. 数学季刊, 2023, 38(3): 311-330.
[11]	黄述亮. 带有对合的素环的微分恒等式[J]. 数学季刊, 2023, 38(2): 134-144.
[12]	马腾. 变指标中心Morrey空间上带Dini核的多线性C-Z算子[J]. 数学季刊, 2023, 38(2): 184-195.
[13]	梁艳霞. 带位势的基尔霍夫方程规范解的存在性[J]. 数学季刊, 2023, 38(2): 196-209.
[14]	白宏芳. 一类具有时滞的生态流行病模型的稳定性与 Hopf 分支[J]. 数学季刊, 2023, 38(2): 157-183.
[15]	杜玲珑, 韩晓岳, 于佳平, 周昕昀. 具有势场的随机Cucker-Smale系统[J]. 数学季刊, 0, (): 111-122.

在复二维仿射锥上的完备余齐性一Kähler度量

Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br#

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价