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Oct 24, 2016 at 8:52 comment added Asaf Shachar OK, it is obvious since the combination is over $C^{\infty}(M)$, not over $\mathbb{R}$.
Oct 24, 2016 at 8:34 comment added Asaf Shachar Sorry, I missed this. Is there a simple reason for why every form can be expressed locally as a combintation of closed forms?
Oct 24, 2016 at 8:12 comment added Sebastian Maybe I could have high-lighten it, but I take $\omega$ to be closed, which is possible.
Oct 24, 2016 at 7:42 comment added Asaf Shachar If I am not mistaken, there should be additional terms in both your equations, which follow from the Leibnitz rule (and involving the derivatives of $\omega$).
Oct 24, 2016 at 7:22 history answered Sebastian CC BY-SA 3.0