|
This article is cited in 7 scientific papers (total in 7 papers)
Complex homogeneous spaces of semisimple Lie groups of the first category
F. M. Malyshev
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 $\widetilde M$. 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.
Received: 09.01.1975
Citation:
F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of the first category”, Math. USSR-Izv., 9:5 (1975), 939–949
Linking options:
https://www.mathnet.ru/eng/im2075https://doi.org/10.1070/IM1975v009n05ABEH001512 https://www.mathnet.ru/eng/im/v39/i5/p992
|
Statistics & downloads: |
Abstract page: | 259 | Russian version PDF: | 78 | English version PDF: | 10 | References: | 46 | First page: | 1 |
|