- #1

tut_einstein

- 31

- 0

I don't understand a particular coordinate expansion of the commutator of 2 vector fields:

[X, Y ]f = X(Y f) − Y (Xf) = X_be_b(Y _ae_af) − Y _be_b(X_ae_af)

= (X_b(e_bY_ a) − Y _b(e_bX_a))e_af + X_aY _b[e_a, e_b]f

X,Y = Vector fields

f = function

X_i = Components of X and same for Y

e_i = coordinates of the vector space

I don't understand how to get the third term in the 2nd line. I can tell that it's probably a product rule but I don't see how to get it.

Thanks!