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
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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
:
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See also Lie differentiation.
How to Cite This Entry:
Lie derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=47628
Lie derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=47628
This article was adapted from an original article by D.V. Alekseevskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article