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:-))

glezen@drb-mathsun1.usc.edu (Paul Glezen) writes:

> "What is the difference between covariant derivative and the Lie 
                                  ^^^^^ D(u,v)                 ^^^ L(u,v) 
>  derivative?"

As you state,
  L(u,v) == [u,v]
On the other hand, 
  D(u,v) - D(v,u) = S(u,v)+[u,v] = S(u,v)+L(u,v)
where S is the torsion 2-form. Therefore the *difference* between D and L
is given by
  D(u,v)-L(u,v)=D(v,u)+S(u,v)
or in a torsion-free spacetime by
  D(v,u),
i.e. the covariant derivative with respect to v of u.

:-))
 Hartmut Frommert                 <phfrom@nyx.uni-konstanz.de>
 Dept of Physics, Univ of Constance, P.O.Box 55 60, D-W-7750 Konstanz, Germany
                                           -- Eat whale killers, not whales --