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 P: 211 Oh, so it's normal for Riemann tensor to be zero since there is no curvature. Phew, I thought I might be doing something wrong xD Is there some easier way of showing that all of the components of Riemann tensor are zero, rather than manually calculating them all? And how come when I look at 2-sphere $g_{\mu \nu} = \begin{pmatrix} r^2 & 0 \\ 0 & r^2\sin^2\theta \end{pmatrix}$ I get several non vanishing components of Riemann tensor? Is it because I'm now looking it from my 3d perspective so I can see that the plane has to be curved to form a sphere?