A family of adapted complexifications for noncompact semisimple Lie groups
arXiv:math/0503377
Abstract
The maximal complexifications adapted to the Levi Civita connection for a distinguished one-parameter family of left-invariant metrics on a real semisimple Lie group G are determined. For G = SL(2,R) their realizations as invariant Riemann domains into SL(2,C) are carried out and their complex-geometric properties are investigated.
34 pages, 6 figures. v2: statement of Prop. 5.4 has changed, minor corrections. v3: revised version, appendix added