= Global potential for cohomologous Kähler forms
{title2=$\widetilde\omega-\omega=i\partial\bar\partial f$}
On a compact <Kähler manifold>, the difference of cohomologous <Kähler forms> is a real, <de Rham cohomology> exact $(1,1)$-form. The <ddbar lemma> gives $\widetilde\omega-\omega=\partial\bar\partial h$. Reality implies $\partial\bar\partial\bar h=-(\widetilde\omega-\omega)$, so $f=(h-\bar h)/(2i)$ is real and has the displayed potential equation. The difference of two real potentials is a <pluriharmonic function>, hence constant on each connected component. On a connected manifold the only ambiguity is one additive constant.
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