Complex homogeneous spaces of semisimple Lie groups of the first category

F. M. Malyshev

Izvestiya. Mathematics , Tome 9 (1975) no. 5, pp. 939-949

Résumé

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 $\widetilde M$. If $G$ is a linear group, then the manifolds $M$ are homogeneous domains in $\widetilde M$; moreover the fibers of the Tits fibration of $\widetilde M$ 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.