曲率与挠率张量的特殊关系

Particular relationship between curvature and torsion tensor

研究挠率和曲率张量在B ianch i恒等式中的相依关系,从Cartan结构方程出发,得到了B ianch i恒等式的三种等价表达形式,局部上和整体上证明了曲率、挠率分量满足的关系式,还揭示了第二B ianch i恒等式的降阶表达形式蕴含的物理意义.

The mutually dependent relations between torsion and curvature tensor in Bianchi identity are studied. From Cantan＇ s structure equations, three equivalent expressions of Bianehi identity are obtained. The behavior of components of torsion and curvature in Bianchi identity is locally revealed. Furthermore, the phisical essence with respect to lower degree expression of the second Bianehi identity is pointed out.