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Pseudoconvex domains spread over complex homogeneous manifolds

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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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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  • DOI: https://doi.org/10.1007/s00229-012-0592-8

Mathematics Subject Classification (2000)

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