We know how objects such as the metric tensor and the Cristoffel symbol have symmetry to them (which is why g(adsbygoogle = window.adsbygoogle || []).push({}); _{12}= g_{21}or [itex]\Gamma[/itex]^{1}_{12}= [itex]\Gamma[/itex]^{1}_{21})

Well I was wondering if the Riemann tensor R^{a}_{bmv}had any such symmetry. Are there any two or more particular indices that I could interchange and still get the same answer? If so, that will save me so much time when deriving these Riemann tensors.

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# Does the Riemann tensor have any symmetry?

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