We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.
Abstract In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω（μ, m）. The first result is that the natural Kahler metric gΩ（μ,m） of Ω（μ, 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 Ω（μ, m）.
