# Contraction in CoordinatesΒΆ

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