Also like affine varieties, we have:

> Theorem. A complex manifold is Stein if and only if it embeds into some $\mathbb{C}^N$ as a closed complex submanifold.

For the "only if" direction, see Hörmander, *An Introduction to Complex Analysis in Several variables*, Theorem 5.3.9. For the converse, <strike> use Cartan B mentioned above. (**Added**: I don't mean to be too pedantic, but Cartan says that $X$ is Stein iff sheaf cohomology vanishes for *coherent analytic* coefficients; it is certainly not true otherwise.)</strike> **Second edit:**  I originally suggested a homological argument for the converse, but it's much easier than that: an argument is contained on pp 109-110  of Hörmander, immediately after the definition of Stein manifold.