Remarks on the canonical metrics on the Cartan–Hartogs domains

Abstract

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. For a Cartan-Hartogs domain Ω B (µ) endowed with the natural Kähler metric g(µ), Zedda conjectured that the coefficient a 2 of the Rawnsley's ε-function expansion for the Cartan-Hartogs domain (Ω B (µ), g(µ)) is constant on Ω B (µ) if and only if (Ω B (µ), g(µ)) is biholomorphically isometric to the complex hyperbolic space. In this paper, following Zedda's argument, we give a geometric proof of the Zedda's conjecture by computing the curvature tensors of the Cartan-Hartogs domain (Ω B (µ), g(µ)).

A Cartan–Hartogs version of the polydisk theorem

“…For this reason Cartan-Hartogs domains represent an important class of domains in C n , and since their first apparence in [28] they have been studied from different points of view, see e.g. [2,6,7,11,12,23,25,29,30].…”

A Cartan-Hartogs version of the Polydisk Theorem

“…For this reason Cartan-Hartogs domains represent an important class of domains in C n , and since their first apparence in [30] they have been studied from different points of view, see e.g. [2,6,7,12,13,25,27,31,32].…”

Geometric Properties of the Pentablock

“…Hartogs domain is a one of important research object in several complex variable. For the studies on Hartogs domain, please refer to [4,5,[16][17][18]. So considering the pentablock P as a Hartogs domain will be great helpful for us to study the convexity of the pentablock P.…”