Balanced metrics on Hartogs domains

摘要

An n-dimensional strictly pseudoconvex Hartogs domain D F can be equipped with a natural Kähler metric g F . In this paper we prove that if m 0 g F is balanced for a given positive integer m 0 then m 0n and (D F ,g F ) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.