Differential Forms, Exterior Derivative I have a question regarding differential forms.
Let $\omega = dx_1\wedge dx_2$.  What would $d\omega$ equal?  Would it be 0?

The differential form $\omega = dx_1 \wedge dx_2$ is constant hence we have $$ d\omega = d(dx_1 \wedge dx_2) = d(1) \wedge dx_1 \wedge dx_2 \pm 1 \, ddx_1 \wedge dx_2 \pm 1 \, dx_1 \wedge ddx_2$$ and because $d^2 = 0$, we have $$ d \omega = 0.$$
