Scalar curvatures in almost Hermitian geometry and some applications  

作　　者：Jixiang Fu Xianchao Zhou 

机构地区：[1]Institute of Mathematics,Fudan University,Shanghai 200433,China [2]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China

出　　处：《Science China Mathematics》2022年第12期2583-2600,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10831008,11025103 and 11501505)。

摘　　要：On an almost Hermitian manifold, there are two Hermitian scalar curvatures associated with a canonical Hermitian connection. In this paper, two explicit formulas on these two scalar curvatures are obtained in terms of the Riemannian scalar curvature, norms of the components of the covariant derivative of the fundamental 2-form with respect to the Levi-Civita connection, and the codifferential of the Lee form. Then we use them to get characterization results of the K?hler metric, the balanced metric, the locally conformal K?hler metric or the k-Gauduchon metric. As corollaries, we show partial results related to a problem given by Lejmi and Upmeier(2020) and a conjecture by Angella et al.(2018).

关 键 词：J-scalar curvature canonical Hermitian connection Hermitian scalar curvature the first Chern form balanced metric k-Gauduchon metric 

分 类 号：O186.12[理学—数学]