Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds.

We study 4-dimensional orientable Riemannian manifolds equipped with a minimal and conformal foliation $${\mathcal {F}}$$ of codimension 2. We prove that the two adapted almost Hermitian structures $$J_1$$ and $$J_2$$ are both cosymplectic if and only if $${\mathcal {F}}$$ is Riemannian and its horizontal distribution $${\mathcal {H}}$$ is integrable. [ABSTRACT FROM AUTHOR]