Vanishing Ricci Tensor in 3 Dimensions

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Airsteve0
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In my general relativity course my professor recommended that it would be useful to convince ourselves that in 3 dimensions the vacuum field equations are trivial because the vanishing of the Ricci tensor implies the vanishing of the full Riemann tensor. However, I am unsure of how to show this mathematically; if someone could help me or point me in the right direction I would appreciate it, thanks.
 

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samalkhaiat
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In my general relativity course my professor recommended that it would be useful to convince ourselves that in 3 dimensions the vacuum field equations are trivial because the vanishing of the Ricci tensor implies the vanishing of the full Riemann tensor. However, I am unsure of how to show this mathematically; if someone could help me or point me in the right direction I would appreciate it, thanks.

Look at
www.physicsforums.com/showthread.php?t=128275
 

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