# Lie derivative

From Encyclopedia of Mathematics

*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.

**How to Cite This Entry:**

Lie derivative. D.V. Alekseevskii (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=13834

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098