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.

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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#

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