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Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle

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Abstract

Let (M,g) be a compact Kahler manifold and (E,F) be a holomorphic Finsler vector bundle of rank r ≥ 2over M. In this paper, we prove that there exists a Kähler metric Φ defined on the projective bundle P(E)of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for Φ having positive scalar curvature is obtained, and a sufficient condition for Φ having positive Ricci curvature is established.

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Acknowledgements

We thank the referees for their valuable time and helpful comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Kun Wang & Chun Ping Zhong

Authors
  1. Kun Wang
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  2. Chun Ping Zhong
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Corresponding author

Correspondence to Chun Ping Zhong.

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Dedicated to Professor Zongyuan Yao for his 80th birthday

Supported by the National Natural Science Foundation of China (Grant No. 11671330)

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Wang, K., Zhong, C.P. Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle. Acta. Math. Sin.-English Ser. 36, 1279–1291 (2020). https://doi.org/10.1007/s10114-020-9296-2

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  • DOI: https://doi.org/10.1007/s10114-020-9296-2

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