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Advanced Physics Homework Help
Riemann Curvature Tensor in 2D
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[QUOTE="Woolyabyss, post: 6166936, member: 426882"] [B]Homework Statement:[/B] Show that the Riemann curvature tensor in 2d is given by ##R_{abcd} =\frac{R}{2}(g_{ac}g_{bd} - g_{ad}g_{bc}) ## [B]Relevant Equations:[/B] ## R = R_{ab} g^{ab} ## and ## R_{ab} = R_{acb}^{c}## Since in 2D the riemman curvature tensor has only one independent component, ## R = R_{ab} g^{ab} ## can be reversed to get the riemmann curvature tensor. Write ## R_{ab} = R g_{ab} ## Now ## R g_{ab} = R_{acbd} g^{cd}## Rewrite this as ## R_{acbd} = Rg_{ab} g_{cd} ## My issue is I'm not sure how they caught a second term? Any help would be appreciated. [/QUOTE]
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Riemann Curvature Tensor in 2D
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