Abstract:
Let G be a connected, real, semisimple Lie group of the first category. In this paper are found all the connected closed subgroups L in G which are such that there exists a complex structure on M=G/L, invariant under the action of G; and also a description is given of all such structures on M. It turns out that the complex homogeneous spaces M thus obtained are covering spaces of homogeneous domains in compact complex homogeneous spaces ˜M. If G is a linear group, then the manifolds M are homogeneous domains in ˜M; moreover the fibers of the Tits fibration of ˜M can only lie entirely in M, and the set of all fibers in M forms a homogeneous domain in the base space of the corresponding Tits fibration.
Bibliography: 16 titles.