摘要
讨论了黎曼流形上半对称度量联络与黎曼联络之间的关系,得到了它们有相同射影曲率张量的充要条件,而且证明了黎曼流形上的半对称度量联络是迷向的,当且仅当它是射影平坦的,这可以认为是贝尔特拉米定理的推广。
In the present paper, the relations between semi-symmetric metric connection and Riemannian connection on a Riemannian manifold ate presented, and the following main results are obtained: (1) In order that a semi-symmetric metric connection D and the Riemannian connection on a Rimsnnian manifold have same projective curvature tensors, it is necessary and sufficient that αx= γgfn. (2) A semi-symmetric metric connection D on a Riemannian manifold is isotropic, if and only if D is projective flat.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
1991年第1期22-24,共3页
Journal of Xiamen University：Natural Science
基金
国家自然科学基金
关键词
半对称联络
迷向
射影平坦
Semi-symmetric connection, Isotropic, Projective flat
