- #1

- 80

- 6

- Summary:
- How is it possible that non-zero components of the curvature tensor depend on theta

I have worked out (and then verified against some sources) that ##R^\theta_{\phi\theta\phi} = sin^2(\theta)##. The rest of the components are either zero or the same as ##R^\theta_{\phi\theta\phi} ## some with the sign flipped.

I was surprised at this, because it implies that the curvature tensor tends to zero as we approach either pole. Being a sphere I thought that the curvature tensor would have the same value everywhere. How can this be?

I was surprised at this, because it implies that the curvature tensor tends to zero as we approach either pole. Being a sphere I thought that the curvature tensor would have the same value everywhere. How can this be?