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Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds

Authors: Filippo Bracci, Andrea Iannuzzi and Benjamin McKay
Journal: Proc. Amer. Math. Soc. 144 (2016), 1619-1629
MSC (2010): Primary 37F75; Secondary 32Q45, 32M10
Published electronically: July 30, 2015
MathSciNet review: 3451238
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Abstract: Let $ M$ be a Kobayashi hyperbolic homogeneous manifold. Let $ \mathcal F$ be a holomorphic foliation on $ M$ invariant under a transitive group $ G$ of biholomorphisms. We prove that the leaves of $ \mathcal F$ are the fibers of a holomorphic $ G$-equivariant submersion $ \pi \colon M \to N$ onto a $ G$-homogeneous complex manifold $ N$. We also show that if $ \mathcal Q$ is an automorphism family of a hyperbolic convex (possibly unbounded) domain $ D$ in $ \mathbb{C}^n$, then the fixed point set of $ \mathcal Q$ is either empty or a connected complex submanifold of $ D$.

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Additional Information

Filippo Bracci
Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133 Roma, Italy

Andrea Iannuzzi
Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133 Roma, Italy

Benjamin McKay
Affiliation: University College Cork, National University of Ireland, Cork, Ireland

Keywords: Kobayashi hyperbolicity, homogeneous manifolds, holomorphic foliation
Received by editor(s): March 3, 2015
Received by editor(s) in revised form: April 23, 2015
Published electronically: July 30, 2015
Additional Notes: The first author was supported by the ERC grant “HEVO - Holomorphic Evolution Equations” n. 277691.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society

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