Covariant derivative and vector functions

[tom.young84]

So given this identity:

[V,W] = $$\nabla$$_VW-$$\nabla$$_WV

^^I got the above identity from O'Neil 5.1 #9.

From this I'm not sure how to make the jump with vector functions, or if it is even possible to apply that definition to a vector function [x_u,x_v].

 

[arkajad]

You question is not clear. Can you be more precise?