在黎曼流形上满足Schur定理的一个半对称射影共形联络  

A semi-symmetric projective conformal connection satisfying the Schur's theorem on a Riemannian manifold

作　　者：许达允 全哲勇 金光植[2] 

机构地区：[1]金日成综合大学数学系 [2]延边大学理学院数学系,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2014年第4期290-294,共5页Journal of Yanbian University（Natural Science Edition）

摘　　要：在黎曼流形上定义了一个半对称射影共形联络,并研究了其性质,同时指出这种联络在特殊情形下可成半对称射影联络、半对称共形联络、对称射影共形联络、射影联络、共形联络以及Levi-Civita联络.在此基础上提出了几种能够满足Schur定理的半对称射影共形联络的形式,并证明半对称射影共形联络的黎曼流形是常曲率黎曼流形的充分必要条件.In Riemannian manifold,we defined a semi-symmetric proj ective conformal connection and consid-ered its properties.In particular cases,this connection reduces to several connections：semi-symmetric proj ec-tive connection,semi-symmetric conformal connection,symmetric proj ective conformal connection,proj ective connection,conformal connection and Levi-Civita connection.We also found forms of a semi-symmetric pro-j ective conformal connection satisfying the Schur’s theorem.And we considered necessary and sufficient condi-tion that a Riemannian manifold with a semi-symmetric proj ective conformal connection be a Riemannian mani-fold with constant curvature.

关 键 词：半对称射影共形联络 半对称射影联络 半对称共形联络 常曲率 

分 类 号：O186.12[理学—数学]