The Lie derivative of tensor 
with respect to the vector
field 
is defined by
 |
(1)
|
Explicitly, it is given by
 |
(2)
|
where 
is a comma derivative. The Lie derivative of
a metric tensor 
with respect to the vector
field 
is given by
 |
(3)
|
where 
denotes the symmetric tensor part and 
is a covariant derivative.
