Manuscripta Mathematica

, Volume 142, Issue 1–2, pp 35–59 | Cite as

Pseudoconvex domains spread over complex homogeneous manifolds

  • Bruce Gilligan
  • Christian Miebach
  • Karl Oeljeklaus
Article

Abstract

Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This is then applied to study the holomorphic reduction of pseudoconvex complex homogeneous manifolds X = G/H. Under the assumption that G is solvable or reductive we prove that X is the total space of a G-equivariant holomorphic fiber bundle over a Stein manifold such that all holomorphic functions on the fiber are constant.

Mathematics Subject Classification (2000)

32M10 (primary) 32E05 32E40 (secondary) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bruce Gilligan
    • 1
  • Christian Miebach
    • 2
  • Karl Oeljeklaus
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada
  2. 2.Laboratoire de Mathématiques Pures et Appliquées,CNRS-FR 2956Université du LittoralCalais CedexFrance
  3. 3.Département de Mathématiques et LATP (UMR-CNRS 6632)Aix-Marseille UniversitéMarseille Cedex 13France

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