Proposition 5.22.3F62C0F30E87C

Proposition 5.22.3.F62C0F30E87C If $\theta =\mathrm{dd}^{\mathrm{c}}\rho $ on an open set for a smooth function $\rho $, then $\mathrm{d}\theta =0$ on that set. In particular, at a point where $\mathrm{d}\theta \neq 0$, no neighborhood admits such a representation.