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## Main Question or Discussion Point

I found the formula for the number of independent components of

Weyl tensor in n-dimensional manifold:

[tex]

(N+1)N/2 - \binom{n}{4} - n(n+1)/2~~~~~N=(n-1)n/2

[/tex]

This expression implies that in 3 dimension Weyl tensor has 0 independent

components, so it's 0. Does it implies that any three-dimensional manifold

is conformally flat (maybe the formula I've written above is incorrect for n<4)?

Weyl tensor in n-dimensional manifold:

[tex]

(N+1)N/2 - \binom{n}{4} - n(n+1)/2~~~~~N=(n-1)n/2

[/tex]

This expression implies that in 3 dimension Weyl tensor has 0 independent

components, so it's 0. Does it implies that any three-dimensional manifold

is conformally flat (maybe the formula I've written above is incorrect for n<4)?