منابع مشابه
Rigidity of Certain Holomorphic Foliations
There is a well-known rigidity theorem of Y. Ilyashenko for (singular) holomorphic foliations in CP and also the extension given by Gómez-Mont and Ort́ız-Bobadilla (1989). Here we present a different generalization of the result of Ilyashenko: some cohomological and (generic) dynamical conditions on a foliation F on a fibred complex surface imply the d-rigidity of F , i.e. any topologically triv...
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The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singu...
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ABSTRACT. Let V be a real hypersurface of class Ck, k ≥ 3, in a complex manifold M of complex dimension n + 1, HT (V ) the holomorphic tangent bundle to V giving the induced CR structure on V . Let θ be a contact form for (V,HT (V )), ξ0 the Reeb vector field determined by θ and assume that ξ0 is of class Ck. In this paper we prove the following theorem (cf. Theorem 4.1): if the integral curves...
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In this paper, we study a notion of hyperbolicity for holomorphic foliations with 1-dimensional parabolic leaves, namely the non-existence of holomorphic cylinders along the foliation – holomorphic maps from D × C to the manifold sending each {∗} × C to a leaf. We construct a tensor, that is a leaf-wise holomorphic section of a bundle above the foliated manifold, which vanishes on an open satur...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2018
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3168