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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=13834
Lie derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_derivative&oldid=13834
This article was adapted from an original article by D.V. Alekseevskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article