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Curl in 2D Manifolds

I'm using SageMath 8.2 on a Windows 10 Native with Jupyter Notebook.

I noticed curl is not defined in a 2D manifold, why is that?

E = Manifold(2, 'E', structure='Riemannian')
cartesian.<x,y> = E.chart()
E.metric()[:] = identity_matrix(2)

v = E.vector_field(name='v')
v[:] = [-x, y^2]
cv = v.curl()
cv.display()


ValueError: the curl is not defined in dimension lower than 3