# Tricky problem

1. Nov 15, 2005

### dextercioby

How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions.

One is given that the Riemann tensor is an (2,2) irreducible rep of $GL(4, \mathbb{R})$ and obeys Bianchi I

$$R_{[\mu\nu|\rho]\lambda}=0$$

Been trying this problem for 3 days and couldn't come up with a reasonable answer.

Daniel.

2. Nov 17, 2005

### BerkMath

(1/12)*n^2*(n^2-1) where n=D.

3. Nov 21, 2005

### dextercioby

Tx, but i found it solved in Nakahara pages 231-232.

Daniel.

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