of a tensor field in the direction of a vector field on a manifold
The tensor field on , of the same type as , given by the formula
where is the local one-parameter group of transformations of the space of tensor fields generated by the vector field . In local coordinates , the Lie derivative of a tensor field of type in the direction of the vector field has coordinates :
See also Lie differentiation.
Lie derivative. D.V. Alekseevskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=13834