In differential geometry, the Lie derivative /ˈliː/, named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate invariant and therefore the Lie derivative is defined on any differentiable manifold. The Lie derivative commutes with contraction and the exterior derivative on differential forms. valid for any vector fields X and Y and any tensor field T.