# Riemann curvature tensor

1. Jul 27, 2013

### Elliptic

1. The problem statement, all variables and given/known data

Show that all components of Riemann curvarue tensor are equal to zero for flat and Minkowski space.

2. Relevant equations

3. The attempt at a solution
$(ds)^2=(dx^1)^2+(dx^2)^2+...+(dx^n)^2 \\ R_{MNB}^A=\partial _{N}\Gamma ^{A}_{MB}-\partial _{M}\Gamma ^{A}_{NB}+\Gamma ^{A}_{NC}\Gamma_{MB}-\Gamma ^{C}_{NB}\Gamma_{MC}$

Last edited: Jul 27, 2013
2. Jul 27, 2013

### WannabeNewton

It's a straightforward problem. What are the Christoffel symbols for Minkowski space-time in the standard coordinates?

3. Jul 27, 2013

### Elliptic

$\Gamma^{K}_{MK}=\frac{1}{2}\left(\partial_Mg_{ML}+\partial_Ng_{ML}-\partial_Lg_{MN} \right )$

Last edited: Jul 27, 2013
4. Jul 27, 2013

### WannabeNewton

Yes but can you tell me why?

5. Jul 27, 2013

### WannabeNewton

Ok but you don't need to edit your posts, you can just reply to my subsequent posts (it makes it easier to keep track of who's saying what). Ok so you know the Christoffel symbols vanish identically because the metric components are constant. So what does that say about the Riemann curvature tensor based on the usual formula?

6. Jul 27, 2013

### Elliptic

That Riemann curvarue tensor is equal to zero?

7. Jul 27, 2013

### WannabeNewton

Yeahp that's it! :)

8. Jul 27, 2013

### Elliptic

Thanks. I have another problem, but i must respect the rules of forum and post a new thread.

9. Jul 27, 2013

Alrighty :)