Beltrami vector field

In vector calculus, a Beltrami vector field, named after Eugenio Beltrami, is a vector field in three dimensions that is parallel to its own curl. That is, F is a Beltrami vector field provided that

Thus ${\displaystyle \mathbf {F} }$ and ${\displaystyle \nabla \times \mathbf {F} }$ are parallel vectors in other words, ${\displaystyle \nabla \times \mathbf {F} =\lambda \mathbf {F} }$.

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