Deformations Feuilletees Des Varietes De Hopf
Complex Variables
2009-02-26 v1
Abstract
In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure along the non-compact leaves is fixed by the complex structure of the compact leaf. Reciprocally, we prove that the complex structure along a non-compact leaf determines the complex structure along the other leaves. We apply these results to the study of foliated deformations of Hopf manifolds, a foliated analogue to the notion of deformation in the large.
Keywords
Cite
@article{arxiv.0902.4301,
title = {Deformations Feuilletees Des Varietes De Hopf},
author = {Laurent Meersseman and Marcel Nicolau and Alberto Verjovsky},
journal= {arXiv preprint arXiv:0902.4301},
year = {2009}
}