Common
Lie derivative
Type of derivative in differential geometry
Lie derivative
In differential geometry, the Lie derivative ( LEE), formulated by Władysław Ślebodziński and named after Sophus Lie, 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. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field, then the Lie derivative of T with respect to X is denoted L X T {\displaystyle {\mathcal {L}}_{X}T} . The differential operator T ↦ L X T {\displaystyle T\mapsto...
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