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for the x-, y-, and z-axes, respectively.

As the name implies the curl is a measure of how much nearby vectors tend in a circular direction.

In Einstein notation, the vector field has curl given by:

where = ±1 or 0 is the Levi-Civita parity symbol.

For a tensor field of order k > 1, the tensor field of order k is defined by the recursive relation

where is an arbitrary constant vector.

A tensor field of order

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