Let $M$ be a symplectic manifold, Then a subbundle $P\subset TM^{\mathbf{C}}$ of the complexified tangent bundle is called a complex polarization if
$P$ is Lagrangian
P involutive
dim$P\cap\bar P \cap TM$ is constant.
Let $P_1, P_2$ be two complex polarization, then when $\bar P_1\cap P_2$ is involutiove ?