Canonical Metrics on Generalized Cartan-Hartogs Domains

In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Omega(mu, m). The first result is that the natural Kahler metric g Omega((mu, m)) of Omega(mu, m) is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Kahler-Einstein metric, the Caratheodary metric, and the Koboyashi metric are equivalent for Omega(mu, m).