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Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds

Author

Listed:
  • Shuwen Li

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

  • Yong He

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

  • Weina Lu

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

  • Ruijia Yang

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

Abstract

Let ( M 1 , g ) and ( M 2 , h ) be two Hermitian manifolds. The twisted product Hermitian manifold ( M 1 × M 2 f , G ) is the product manifold M 1 × M 2 endowed with the Hermitian metric G = g + f 2 h , where f is a positive smooth function on M 1 × M 2 . In this paper, the Chern curvature, Chern Ricci curvature, Chern Ricci scalar curvature and holomorphic sectional curvature of the twisted product Hermitian manifold are derived. The necessary and sufficient conditions for the compact twisted product Hermitian manifold to have constant holomorphic sectional curvature are obtained. Under the condition that the logarithm of the twisted function is pluriharmonic, it is proved that the twisted product Hermitian manifold is Chern flat or Chern Ricci-flat, if and only if M 1 , g and M 2 , h are Chern flat or Chern Ricci-flat, respectively.

Suggested Citation

  • Shuwen Li & Yong He & Weina Lu & Ruijia Yang, 2024. "Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds," Mathematics, MDPI, vol. 12(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:449-:d:1329912
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    References listed on IDEAS

    as
    1. Qihui Ni & Yong He & Jinhua Yang & Hui Zhang & Mehmet Atçeken, 2022. "Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-7, July.
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