# 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

Reference: The Divergence and Curl of a Vector Field In Two Dimensions