Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds

Shuwen Li, Yong He (), Weina Lu and Ruijia Yang
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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

Mathematics, 2024, vol. 12, issue 3, 1-12

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.

Keywords: Hermitian manifold; twisted product; holomorphic sectional curvature; Chern flat; Chern Ricci-flat (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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