In Theorems 6.3 and 6.4 we give an analogue of Theorem 5.1 to characterize
the smoothly bounded, relatively compact pseudoconvex domains D in a complex
homogeneous space M which are Stein. We immediately apply this result to special
Hopf manifolds Hn. Then in section 7 we apply the result to describe all of the
non-Stein pseudoconvex domains D in complex flag spaces Fn (Theorem 7.1).
Some of the results in this paper were announced without proof in [12] and
[10]; in this paper, we provide complete proofs and illustrate the significance of
this generalization of the second variation formula with applications and concrete
examples. The material presented is completely self-contained; in particular, all
concepts pertaining to Lie theory and homogeneous spaces are explained.
We thank Professor T. Ueda for his helpful advice in our study of Levi problems
for flag spaces. We also thank Professor T. Morimoto for his useful comments
regarding Lie algebras and the referee for constructive remarks.
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