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 Duan ,
  • Zhuangdan Guan
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  • 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
Xiaoman Duan, E-mail: xiaomanduanhenu@163.com

Received date: 2022-07-08

  Revised date: 2023-07-15

  Online published: 2024-02-27

Supported by

NSFC (12171140).

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.

Cite this article

Xiaoman Duan , Zhuangdan Guan . COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES (RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)*[J]. Acta mathematica scientia, Series B, 2024 , 44(1) : 78 -102 . DOI: 10.1007/s10473-024-0103-5

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