Deformations Feuilletees Des Varietes De Hopf
Laurent Meersseman (IMB), Marcel Nicolau, Alberto Verjovsky

TL;DR
This paper studies special foliations with complex leaves, showing how the complex structure of a compact leaf determines the structure of non-compact leaves and vice versa, with applications to Hopf manifolds.
Contribution
It establishes a reciprocal relationship between the complex structures of compact and non-compact leaves in certain foliations and applies this to deformations of Hopf manifolds.
Findings
Complex structure along non-compact leaves is fixed by the compact leaf's structure.
The complex structure on one non-compact leaf determines all others.
Results provide insights into foliated deformations of Hopf manifolds.
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.
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Taxonomy
TopicsMathematics and Applications
