数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 78-102.doi: 10.1007/s10473-024-0103-5

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COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES (RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)*

Xiaoman Duan1, Zhuangdan Guan1,2,†   

  1. 1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China;
    2. Department of Mathematics, The University of California at Riverside, Riverside, CA 92521, USA
  • 收稿日期:2022-07-08 修回日期:2023-07-15 出版日期:2024-02-25 发布日期:2024-02-27
  • 通讯作者: † Zhuangdan Guan, E-mail: guan@henu.edu.cn
  • 作者简介:Xiaoman Duan, E-mail: xiaomanduanhenu@163.com
  • 基金资助:
    NSFC (12171140).

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES (RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)*

Xiaoman Duan1, Zhuangdan Guan1,2,†   

  1. 1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China;
    2. Department of Mathematics, The University of California at Riverside, Riverside, CA 92521, USA
  • Received:2022-07-08 Revised:2023-07-15 Online:2024-02-25 Published:2024-02-27
  • Contact: † Zhuangdan Guan, E-mail: guan@henu.edu.cn
  • About author:Xiaoman Duan, E-mail: xiaomanduanhenu@163.com
  • Supported by:
    NSFC (12171140).

摘要: In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

关键词: Kähler Metrics, complete Riemannian metrics, open complex manifolds, holomorphic bisectional curvature, $C^*$ bundle, almost homogeneous manifolds

Abstract: In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

Key words: Kähler Metrics, complete Riemannian metrics, open complex manifolds, holomorphic bisectional curvature, $C^*$ bundle, almost homogeneous manifolds

中图分类号: 

  • 53C10