Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 69-77

First online:

Balanced metrics on Hartogs domains

  • Andrea LoiAffiliated withDipartimento di Matematica e Informatica, Università di Cagliari Email author 
  • , Michela ZeddaAffiliated withDipartimento di Matematica e Informatica, Università di Cagliari

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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.

Keywords

Kähler metrics Balanced metrics Hartogs domains

Mathematics Subject Classification (2000)

53C55 58C25