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Pseudoconvex domains spread over complex homogeneous manifolds

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina, Regina, S4S 0A2, Canada

    Bruce Gilligan

  2. Laboratoire de Mathématiques Pures et Appliquées,CNRS-FR 2956, Université du Littoral, 50, Rue F. Buisson, 62228, Calais Cedex, France

    Christian Miebach

  3. Département de Mathématiques et LATP (UMR-CNRS 6632), Aix-Marseille Université, 39, Rue F. Joliot-Curie, 13453, Marseille Cedex 13, France

    Karl Oeljeklaus

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  1. Bruce Gilligan
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  2. Christian Miebach
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  3. Karl Oeljeklaus
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Correspondence to Karl Oeljeklaus.

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Gilligan, B., Miebach, C. & Oeljeklaus, K. Pseudoconvex domains spread over complex homogeneous manifolds. manuscripta math. 142, 35–59 (2013). https://doi.org/10.1007/s00229-012-0592-8

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