Homogeneous hyperbolic manifolds and homogeneous Siegel domains
It is proved that a hyperbolic manifold admitting a transitive action of a Lie group is isomorphic to a homogeneous Siegel domain of second kind. As a consequence such a manifold is biholomorphic to a bounded homogeneous domain. This solves a problem posed by \textit{S. Kobayashi} in ''Hyperbolic manifolds and holomorphic mapping'' (1970; Zbl 0207.379).
homogeneous Siegel domain of second kind
scientific article; zbMATH DE number 3933488