PSEUDOCONVEX DOMAINS SPREAD OVER COMPLEX HOMOGENEOUS MANIFOLDS. - Archive ouverte HAL Access content directly
Journal Articles Manuscripta mathematica Year : 2012

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 pseu- doconvex 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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Dates and versions

hal-01066246 , version 1 (19-09-2014)

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Bruce Gilligan, Christian Miebach, Karl Oeljeklaus. PSEUDOCONVEX DOMAINS SPREAD OVER COMPLEX HOMOGENEOUS MANIFOLDS.. Manuscripta mathematica, 2012, 142, pp.35-59. ⟨10.1007/s00229-012-0592-8⟩. ⟨hal-01066246⟩
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