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arXiv · 1204.1163

Pseudoconvex domains spread over complex homogeneous manifolds

Bruce Gilligan·Christian Miebach·Karl Oeljeklaus
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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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Bruce Gilligan, Christian Miebach, Karl Oeljeklaus. 2012-04-05. Pseudoconvex domains spread over complex homogeneous manifolds. https://doi.org/10.1007/s00229-012-0592-8

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