Primitive of an Exact form I have the following differential $3$-form,
$$ H = \cos \zeta \sin \zeta\, \mathrm{d}\zeta \wedge \mathrm{d}\varphi_1 \wedge \mathrm{d}\varphi_2 $$
which I know is exact by the properties of my problem.
Now I would like to find a primitive form $B$ such that $H = \mathrm{d}B$.
I figured out it will depend on the cosine of the difference $\varphi_1 -\varphi_2$ (such that the derivative with respect the two angles will disappear at the end. But I don't manage to do the formal complete calculation. Any idea?

Why not trying to write something like
\begin{equation}
B=B_{1} (\zeta,\varphi_1,\varphi_2)\mathrm{d}\varphi_1 \wedge \mathrm{d}\varphi_2+B_{2}(\zeta,\varphi_1,\varphi_2)\mathrm{d}\zeta \wedge \mathrm{d}\varphi_1+B_{3}(\zeta,\varphi_1,\varphi_2)\mathrm{d}\zeta \wedge \mathrm{d}\varphi_2
\end{equation}
If $H=dB$ is exact, you may find constraints on each $B_{i}$.
