Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (2): 200-220.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.008

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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 Daniel1,2, LIANG Meng-xiang1   

  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.
  • 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).

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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.

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