On neighborhoods of embedded toroidal and Hopf manifolds and their foliations

Abstract

In this article, we give completely new examples of embedded complex manifolds the germ of neighborhood of which is holomorphically equivalent to a germ of neighborhood of the zero section in its normal bundle. The first set of examples is composed of connected abelian complex Lie groups, embedded in some complex manifold $M$. These are non compact manifolds in general. We also give some conditions ensuring the existence a holomorphic foliation having the embedded manifold as leaf. The second set of examples are $n$-dimensional Hopf manifolds, embedded as hypersurfaces.