Classification of holomorphic foliations on Hopf manifolds

TL;DR

This paper classifies nonsingular holomorphic foliations on Hopf manifolds, proving integrability and existence of holomorphic first integrals for codimension one distributions, and explores properties of singular distributions.

Contribution

It provides a complete classification of nonsingular holomorphic foliations on Hopf manifolds and establishes integrability results for codimension one distributions.

Findings

All nonsingular codimension one distributions on certain Hopf manifolds are integrable.

Such distributions have holomorphic integral first.

Results on properties of singular holomorphic distributions on Hopf manifolds.

Abstract

We classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable and has holomorphic integral first. Also, we prove some results about singular holomorphic distributions on Hopf manifolds.