Totally real embeddings with prescribed polynomial hulls

We embed compact $C^{\mathrm{\infty }}$ manifolds into ${\mathbb{C}}^n$ as totally real manifolds with prescribed polynomial hulls. As a consequence we show that any compact $C^{\mathrm{\infty }}$ manifold of dimension $d$ admits a totally real embedding into ${\mathbb{C}}^{\lfloor \frac{3d}{2}\rfloor }$ with non-trivial polynomial hull without complex structure.