Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds

Details Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds

2011-11-30

arxiv.org/abs/1111.7118v2

Mathematics

Complex Variables

Version 2: using Nakajima's results instead of Winkelmann's classification of homogeneous spaces of low dimension, we are able

Scientific paper

Let $M=G/H$ be a Kobayashi hyperbolic, homogeneous complex manifold endowed
with a non-singular, $G$-invariant, holomorphic foliation $\mathcal F$. We show
that $M$ is biholomorphic to the product $D\times F$ of two (simply connected)
bounded homogeneous domains and the foliation $\mathcal F$ is given by the
natural projection $M\to D$.

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