A family of adapted complexifications for $S{L}_2\left(ℝ\right)$

Halverscheid, Stefan; Iannuzzi, Andrea

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 17-49.

Let $G$ be a non-compact, real semisimple Lie group. We consider maximal complexifications of $G$ which are adapted to a distinguished one-parameter family of naturally reductive, left-invariant metrics. In the case of $G=S{L}_2\left(ℝ\right)$ their realization as equivariant Riemann domains over $G^{ℂ}=S{L}_2\left(ℂ\right)$ is carried out and their complex-geometric properties are investigated. One obtains new examples of non-univalent, non-Stein, maximal adapted complexifications.

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