San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

The Riemann-Christoffel Tensor

The Riemann-Christoffel tensor arises as the difference of cross covariant derivatives. Let Ai be any covariant tensor of rank one. Then

Ai, jk − Ai, kj = RijkpAp

Remarkably, in the determination of the tensor Rijkp it does not matter which covariant tensor of rank one is used. The tensor Rijkp is called the Riemann-Christoffel tensor of the second kind. As the notation indicates it is a mixed tensor, covariant of rank 3 and contravariant of rank 1. This has to be proven.

The determination of the nature of Rijkp goes as follows.

(To be continued.)

HOME PAGE OF applet-magic
HOME PAGE OF Thayer Watkins