This work continues a previous study by Hounie and Zugliani on the global solvability of a locally integrable structure of tube type and a corank one, considering a linear partial differential operator
L
\mathbb L
associated with a real analytic closed
1
1
-form defined on a real analytic closed
n
n
-manifold. We deal now with a general complex form and complete the characterization of the global solvability of
L
.
\mathbb L.
In particular, we state a general theorem, encompassing the main result of Hounie and Zugliani.
As in Hounie and Zugliani’s work, we are also able to characterize the global hypoellipticity of
L
\mathbb L
and the global solvability of
L
n
−
1
\mathbb L^{n-1}
—the last nontrivial operator of the complex when
M
M
is orientable—which were previously considered by Bergamasco, Cordaro, Malagutti, and Petronilho in two separate papers, under an additional regularity assumption on the set of the characteristic points of
L
.
\mathbb L.