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## Main Question or Discussion Point

hi, I am just curious about, and really wonder if there is a proof which demonstrates that curvature tensor is 0 in all flat space coordinates. Nevertheless, I have seen the proofs related to curvature tensor in Cartesian coordinates and polar coordinates, but have not been able to see that zero curvature tensor dominates all flat space coordinates ( besides the polar and cartesian coordinates ). Could you please explain or help me reach the proof ???