Calculating Riemann Tensor for S^2 with Pull-Back Metric from Euclidean Space

[Mathman_]

Find the Riemann tensor of the 2-sphere of radius r

S^{2}_{r}={(x,y,z) \in\Re^{3}|x^{2} + y^{2} + z^{2} = r^{2}}

with metric g obtained as the pull-back of the Euclidean metric g_R3 by the inclusion
map S^{2} \hookrightarrow\Re^{3}.

Any help would be appreciated. Thanks

 

[AEM]

This seems to be a pretty straight forward problem. Rewrite your metric in spherical coordinates. Identify your g_{\mu \nu}. Go to a book on General Relativity and find the definition of the Riemann tensor in terms of the Christoffel symbols and calculate it out. It will take a little time, but it's not hard.