Contraction in Coordinates¶
Given a manifold , the interior product is defined as the contraction of a differential form with a vector field.
The contraction of a one-form with a vector field is given by
The contraction of a two-form with the same vector field is given by
The contraction of a three-form is going to be
In 2D the explicit formula for the contractions are
If 3D, on the other hand, the contractions become