Global Stability for Holomorphic Foliations in Kaehler Manifolds

Abstract

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems for compact foliations in Kaehler manifolds of Edwards-Millett-Sullivan and Hollman.

3 pages

Cited by in corpus (3)

• A global Weinstein splitting theorem for holomorphic Poisson manifolds
• Uniformizable foliated projective structures along singular foliations
• The structure of uniruled manifolds with split tangent bundle