Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE CHERN SECTIONAL CURVATURE OF A HERMITIAN MANIFOLD

  • Pandeng Cao (School of Mathematical Sciences Xiamen university) ;
  • Hongjun Li (School of Mathematics and Statistics Henan University)
  • Received : 2023.02.07
  • Accepted : 2024.02.29
  • Published : 2024.07.31
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Abstract

On a Hermitian manifold, the Chern connection can induce a metric connection on the background Riemannian manifold. We call the sectional curvature of the metric connection induced by the Chern connection the Chern sectional curvature of this Hermitian manifold. First, we derive expression of the Chern sectional curvature in local complex coordinates. As an application, we find that a Hermitian metric is Kähler if the Riemann sectional curvature and the Chern sectional curvature coincide. As subsequent results, Ricci curvature and scalar curvature of the metric connection induced by the Chern connection are obtained.

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Acknowledgement

The authors are very grateful to the referee for providing many helpful suggestions that substantially improved the manuscript. The authors gratefully acknowledge the financial supports by the National Science Foundation of China under Grant No. 12001165.

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