A Stein manifold is a complex manifold which admits a proper
holomorphic embedding into a complex Euclidean space. Examples
include open Riemann surfaces and domains of holomorphy over $C^n$.
Every n-dimensional Stein manifold admits a holomorphic immersion
into $C^k$ with $k=[3n/2]$, but in general not to a lower dimensional
space. In this talk I will discuss progress on the following
outstanding classical problem:
Does every n-dimensional Stein manifold with trivial tangent bundle
admit a holomorphic immersion to $C^n$ ?