A note on homogeneous hyperbolic manifolds (Q1065212)

It is proved that a hyperbolic manifold admitting a transitive action of a solvable Lie group is isomorphic to a bounded homogeneous domain in \({\mathbb{C}}^ n.\) Recently the author generalized this result to an arbitrary transitive Lie group action [the author: ''Homogeneous hyperbolic manifolds and homogeneous Siegel domains'', preprint.] Therefore one of the problems posed by \textit{S. Kobayashi} in ''Hyperbolic manifolds and holomorphic mappings'', (1970; Zbl 0207.379) is solved.