Harmonic Currents of Finite Energy and Laminations, J. E. Fornaess and N. Sibony, Geometric And Functional Analysis, $2005$, Page $965$, Section $2$ "Harmonic Currents".
Definition $2.1$
Let $M$ be a Compact Complex Manifold of (complex) dimension $k$. For $0\leqslant p,q \leqslant k$, let $T$ be a $(p,q)$ current on $M$ of order $0$. We say that $T$ is Harmonic if $i\partial \overline{\partial} T=0$.
The question is:
Is not it enough in the definition of Harmonic Current to say $\partial \overline{\partial} T=0$ (without $i$) that means the current is $\partial \overline{\partial} -$ closed? (Why did they add $i$ in the definition?).
