A family of adapted complexifications for SL2(R)

Abstract

Let G be a non-compact, real semisimple Lie group. We consider maximal complexifications of G which are adapted to a distinguished oneparameter family of naturally reductive, left-invariant metrics. In the case of G = SL 2 (R) their realization as equivariant Riemann domains over G C = SL 2 (C) is carried out and their complex-geometric properties are investigated. One obtains new examples of non-univalent, non-Stein, maximal adapted complexifications.