  We consider the question if a five dimensional manifold can be embedded into
a Calabi-Yau manifold of complex dimension three such that the real part of the
holomorphic volume form induces a given closed 3-form on the 5-manifold. We
define an open set of 3-forms in dimension five which we call strongly
pseudoconvex, and show that for closed strongly pseudoconvex 3-forms the
perturbative version of this embedding problem can be solved if a finite
dimensional vector space of obstructions vanishes.
