If , are vector fields on a manifold and , differentiable functions, show that
Also if , , are vector fields on , calculate the components of , , .
Finally, let be a map of the -dimensional manifold and , be two dimensional fields onto . If are the basic vector fields of and , where , show that .
( denotes the Lie bracket on vector fields) I am not familiar with the Lie bracket at all, so I would be happy if someone helped!