In this article we use the twistor theory in order to build ``non standard'' complex structures (with a meaning which we define) on the products of $4$-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is $\mathcal C^\infty$-trivial. Among these surface we will study those which admit an anti-self-dual riemannian metric.
Guillaume Deschamps. "Espaces twistoriels et structures complexes non standards." Publ. Mat. 52 (2) 435 - 457, 2008.