Lie derivative

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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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098