A family of adapted complexifications for noncompact semisimple Lie groups

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.

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