HO Talyun,JEN Cholyong,JIN Guangzhi*.A semi-symmetric projective conformal connection satisfying the Schur’s theorem on a Riemannian manifold[J].Journal of Yanbian University,2014,40(04):290-294.
在黎曼流形上满足Schur定理的一个半对称射影共形联络
- Title:
- A semi-symmetric projective conformal connection satisfying the Schur’s theorem on a Riemannian manifold
- Keywords:
- semi-symmetric projective conformal connection; semi-symmetric projective connection; semi-symmetric conformal connection; constant curvature
- 分类号:
- O186.12
- 文献标志码:
- A
- 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.
- Abstract:
- In Riemannian manifold, we defined a semi-symmetric projective conformal connection and considered its properties. In particular cases, this connection reduces to several connections: semi-symmetric projective connection, semi-symmetric conformal connection, symmetric projective conformal connection, projective connection, conformal connection and Levi-Civita connection. We also found forms of a semi-symmetric projective conformal connection satisfying the Schur’s theorem. And we considered necessary and sufficient condition that a Riemannian manifold with a semi-symmetric projective conformal connection be a Riemannian manifold with constant curvature.
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备注/Memo
收稿日期: 2014-10-22*通信作者: 金光植(1958—),男,副教授,研究方向为应用统计学.