Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature  

作　　者：Pei Pei RAO Fang Yang ZHENG 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第6期1094-1104,共11页数学学报（英文版）

基　　金：supported by NSFC(Grant No.12071050);Chongqing Normal University。

摘　　要：A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kèahler when the constant is non-zero and must be Chern flat when the constant is zero.The conjecture is known in complex dimension 2 by the work of Balas-Gauduchon in 1985(when the constant is zero or negative)and by Apostolov±Davidov±Muskarov in 1996(when the constant is positive).For higher dimensions,the conjecture is still largely unknown.In this article,we restrict ourselves to pluriclosed manifolds,and confirm the conjecture for the special case of Strominger Kèahler-like manifolds,namely,for Hermitian manifolds whose Strominger connection(also known as Bismut connection)obeys all the Kaèhler symmetries.

关 键 词：Pluriclosed manifold Hermitian manifold Strominger connection holomorphic sectional curvature 

分 类 号：O186[理学—数学]