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$U,V$ vector fields on $\mathbb{R}^3$ $$U = \frac{\partial}{\partial x},V = F\frac{\partial}{\partial y}+G\frac{\partial}{\partial z}$$ answer key says: $$[U,V] = F_x\frac{\partial}{\partial y}+G_x\frac{\partial}{\partial z} $$ By my calculations, given $f:\mathbb{R}^3\rightarrow\mathbb{R}$ smooth (I can't get the align environment to work for some reason) $$[U,V](f)\\ U(V(f))-V(U(f))\\ test $$
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Sun, 17 Dec 2017 04:21 GMT