Canonical metrics on generalized Cartan-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 Kähler metric g ^{Ω(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 Kähler-Einstein metric, the Carathéodary metric, and the Koboyashi metric are equivalent for Ω(μ, m).

Keywords

Canonical metric / Extremal metric / Comparison theorem / Generalized Cartan-Hartogs domains

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