Induced local actions on taut and Stein manifolds

Abstract

Let G = ( R , + ) G=({\mathbb {R}},+) act by biholomorphisms on a taut manifold X X . We show that X X can be regarded as a G G -invariant domain in a complex manifold X ∗ X^{*} on which the universal complexification ( C , + ) ({\mathbb {C}},+) of G G acts. If X 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 ∗ X^{*} is discussed.