Date: 21 Jan 2011

Balanced metrics on Hartogs domains

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Abstract

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 0>n and (D F ,g F ) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.

Communicated by V. Cortés.
The first author was supported by the M.I.U.R. Project ‘‘Geometric Properties of Real and Complex Manifolds”; the second author was supported by RAS through a grant financed with the “Sardinia PO FSE 2007-2013” funds and provided according to the L.R. 7/2007.