DEFORMATIONS FEUILLETEES DES VARIETES DE HOPF

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [13 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00363022
Contributor : Laurent Meersseman <>
Submitted on : Friday, February 20, 2009 - 10:46:37 PM
Last modification on : Thursday, October 11, 2018 - 1:46:04 PM
Long-term archiving on : Tuesday, June 8, 2010 - 10:44:02 PM

Files

deffeuil.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00363022, version 1
  • ARXIV : 0902.4301

Collections

Citation

Laurent Meersseman, Marcel Nicolau, Alberto Verjovsky. DEFORMATIONS FEUILLETEES DES VARIETES DE HOPF. 2009. ⟨hal-00363022⟩

Share

Metrics

Record views

333

Files downloads

244