- #1

Woolyabyss

- 143

- 1

- Homework Statement:
- Show that the Riemann curvature tensor in 2d is given by ##R_{abcd} =\frac{R}{2}(g_{ac}g_{bd} - g_{ad}g_{bc}) ##

- Relevant Equations:
- ## 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.

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.