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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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy

    Andrea Loi & Michela Zedda

Authors
  1. Andrea Loi
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  2. Michela Zedda
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Corresponding author

Correspondence to Andrea Loi.

Additional information

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.

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Loi, A., Zedda, M. Balanced metrics on Hartogs domains. Abh. Math. Semin. Univ. Hambg. 81, 69–77 (2011). https://doi.org/10.1007/s12188-011-0048-1

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  • DOI: https://doi.org/10.1007/s12188-011-0048-1

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