Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds

Abstract

Let $M$ be a Kobayashi hyperbolic homogenous 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 $\pi :M\to N$ 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 $D$.

final version

References in corpus (1)

• Quotients of bounded homogeneous domains by cyclic groups