A family of adapted complexifications for noncompact semisimple Lie groups

Details A family of adapted complexifications for noncompact semisimple Lie groups A family of adapted complexifications for noncompact semisimple Lie groups

2005-03-18

arxiv.org/abs/math/0503377v3

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol VIII (2009), 17-49

Mathematics

Complex Variables

34 pages, 6 figures. v2: statement of Prop. 5.4 has changed, minor corrections. v3: revised version, appendix added

Scientific paper

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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