On neighborhoods of embedded toroidal and Hopf manifolds and their foliations

Laurent Stolovitch; Xiaojun Wu

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arXiv · 2510.26454

On neighborhoods of embedded toroidal and Hopf manifolds and their foliations

Laurent Stolovitch·Xiaojun Wu

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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.

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Laurent Stolovitch, Xiaojun Wu. 2025-10-30. On neighborhoods of embedded toroidal and Hopf manifolds and their foliations. https://arxiv.org/abs/2510.26454

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