Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 525-539.doi: 10.1007/s10473-025-0214-7

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EXISTENCE OF SOME SPECIAL CONFORMALLY-KÄHLER METRICS ON CERTAIN CP1 BUNDLES

Jing Chen1, Daniel 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:2023-08-23 Revised:2024-07-17 Online:2025-03-25 Published:2025-05-08
  • Contact: *Daniel Guan, E-mail: guan@henu.edu.cn
  • About author:Jing Chen, E-mail: chenj@henu.edu.cn
  • Supported by:
    This research was supported by the Nature Science Foundation of China (12171140).

Abstract: In this paper, we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kähler metric related to a metric in any given Kähler class for any k2.

Key words: Hermitian metrics, conformally-Kähler metrics, complex manifolds, scalar curvature, fiber bundle, almost homogeneous manifolds

CLC Number: 

  • 53C10
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