Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature

作     者：Pei Pei RAO Fang Yang ZHENG Pei Pei RAO;Fang Yang ZHENG

作者机构：School of Mathematical SciencesChongqing Normal UniversityChongqing 401331P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第6期

页      面：1094-1104页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

主　　题：Pluriclosed manifold Hermitian manifold Strominger connection holomorphic sectional curvature 

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 *** 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 *** 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.