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Riemann curvature tensor

Ricci tensor

{c}
{title2=$S_{ij}=\frac1{n-2}(R_{ij}-\frac{R}{2(n-1)}g_{ij})$}

For dimension $n\geq3$, the Schouten tensor packages the <Ricci tensor> and <scalar curvature> in the trace part of the <Riemann curvature tensor>. In dimension three it is $S_{ij}=R_{ij}-Rg_{ij}/4$, and the full <Riemann curvature tensor> is reconstructed from it.

Schouten tensor

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 51 / 3 / Solution

Three-dimensional curvature from the Ricci tensor

Schouten tensor ( $S_{ij} = \frac{1}{n - 2} (R_{ij} - \frac{R}{2 ( n - 1 )} g_{ij})$ )

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Schouten tensor (Sij​=n−21​(Rij​−2(n−1)R​gij​))

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Schouten tensor ( $S_{ij} = \frac{1}{n - 2} (R_{ij} - \frac{R}{2 ( n - 1 )} g_{ij})$ )

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