Equation 11.2.208B6CFC8EA37B

\begin{equation} \begin{aligned} H_\omega (\mathrm{dd}^{\mathrm{c}}\varphi ,\mathrm{dd}^{\mathrm{c}}\varphi ) & =-\frac12\int _ X\omega ^2\wedge (\mathrm{dd}^{\mathrm{c}}\varphi )^2\\ & =\frac12\int _ X\mathrm{dd}^{\mathrm{c}}(\omega ^2)\wedge \mathrm d\varphi \wedge \mathrm d^{\mathrm c}\varphi . \end{aligned} \end{equation}