I just asked the following question at stackoverflow :

http://stackoverflow.com/questions/33453941/determining-christoffel-symbols-and-curvature-tensors-for-a-flat-sphere-using-sy

In essence, the question is two fold :

1) My own implementation fails for flat surfaces in 3D
2) Sympy.Diffgeom seems to give wrong results

Really appreciate any insight as to what is causing the error and why the 
hand-coded sympy.diffgeom produces wrong result.

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