Independent components of the Riemann tensor

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This video investigates the symmetry properties of the Riemann tensor and uses those properties to determine the number of independent components it possesses in a given n-dimensional space. It does this by looking at the possible combinations of values the indices can take given the symmetry properties this tensor possesses.

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I was stuck trying to find a way to get the number of indipendents components for hours, this video is by far the most useful thing I've found on youtube

olderspice

Thanks for this video..
I was stuck on this for some time

sayantanpoali

Thank the universe for this video!!! It helped a lot.

zmaglif

why the ciclicity reduces components of a factor 2/3? thanks for video!

pippomio

How about this?
1. Antisymmetric property of the Riemann curvature tensor >> n(n-1)/2
2. Symmetric property of the Christoffel symbol >> n(n+1)/2
ㄴSince we made Riemann tensor using the Christoffel symbol.
3. Jacobi Identity of the Riemann curvature tensor >> 1/3
Finally, n^2 (n^2 -1)/12

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