Hi, thanks for the attention and excuse for my bad english.(adsbygoogle = window.adsbygoogle || []).push({});

I'm studying general relativity and I have a doubt about the number of indipendent component of the riemann curvature tensor.

We have two kind of riemann tensor:

type (3,1) R^{i}_{kml}

type (4,0) R_{rkml}

There are also some symmetry rule:

first skew-symmetryRsecondo skew-symmetry_{rkml}= -R_{krml}R_{rkml}= -R_{rklm}(Rblock symmetry^{i}_{kml}= -R^{i}_{klm})RBianchi's first identity_{rkml}= R_{mlrk}R_{rkml}+R_{rlkm}+R_{rmlk}=0(R^{i}_{kml}+R^{i}_{lkm}+R^{i}_{mlk}=0)

Now, the (4,0) R-type has

n^{2}(n^{2}-1)/12

indipendent components. What about the (3,1) R-type? The indipendent component are also n^{2}(n^{2}-1)/12 or they are n^{2}(n^{2}-1)/3?

(In the case n=4, (4,1) R-type has 20 indipendent component; (3,1) R-type are 20 or 80?)

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# Riemann tensor: indipendent components

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