Induced local actions on taut and Stein manifolds

Abstract:

Let $G=({\mathbb {R}},+)$ act by biholomorphisms on a taut manifold $X$. We show that $X$ can be regarded as a $G$-invariant domain in a complex manifold $X^{*}$ on which the universal complexification $({\mathbb {C}},+)$ of $G$ acts. If $X$ is also Stein, an analogous result holds for actions of a larger class of real Lie groups containing, e.g., abelian and certain nilpotent ones. In this case the question of Steinness of $X^{*}$ is discussed.