I know that the Riemann tensor vanishes in a flat space. And no amount of co-ordinate transformations can go from a flat space to a curved space.(adsbygoogle = window.adsbygoogle || []).push({});

Does that mean there is no transformation that will go from, say Cartesian 2D, to [itex](\theta,\phi)[/itex], the co-ordinates usually used for the unit 2-sphere? I say this since the first space is flat, and the second is curved.

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# Transforming to curved manifolds

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