Results 11 to 20 of about 7,311 (162)
On deformations of holomorphic foliations [PDF]
Annales de l'Institut Fourier, 1989 Given a non-singular holomorphic foliation ℱ on a compact manifold M we analyze the relationship between the versal spaces K and K tr of deformations of ℱ as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of ℱ parametrized by an analytic space K f ...
Joan Girbau, Marcel Nicolau
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Abelian integrals in holomorphic foliations [PDF]
Revista Matemática Iberoamericana, 2002 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.
Hossein Movasati
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Topological rigidity for holomorphic foliations [PDF]
, 2007 We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_ }$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a foliation $\mathcal{F}_0$ on $\mathbb{C}^2$.
Mahdi Teymuri Garakani
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Complete nonsingular holomorphic foliations on Stein manifolds [PDF]
Mediterranean Journal of Mathematics, 2023 AbstractLet X be a Stein manifold of complex dimension $$n>1$$ n > 1 endowed with a Riemannian metric $${\mathfrak {g}}$$ g .
Antonio Alarcón, Franc Forstnerič
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Stability Theorems for Holomorphic Foliations [PDF]
Transactions of the American Mathematical Society, 1980 Here we investigate topological stability in the space of holomorphic foliations on a compact manifold. We show that under certain conditions nearby holomorphic foliations are topologically equivalent. We then present examples of foliations which are stable as holomorphic foliations but unstable as smooth foliations.
Duchamp, T., Kalka, M.
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A residue formula for holomorphic foliations. [PDF]
Michigan Mathematical Journal, 1980 James L. Heitsch
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Holomorphic foliations and deformations of the Hopf foliation [PDF]
Pacific Journal of Mathematics, 1984 A deformation theory for transversally holomorphic foliations is developed here and used to give an explicit description of the transver- sally holomorphic foliations near the "Hopf foliations" on odd dimen- sional spheres. Introduction. In (1) and (2) we began the study of the deformation theory of holomorphic foliations on a smooth compact manifold ...
Duchamp, T., Kalka, M.
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Unfoldings of holomorphic foliations [PDF]
Publicacions Matemàtiques, 2021 The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.
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Codimension two holomorphic foliation
Journal of Differential Geometry, 2019 This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the existence of codimension two foliations which are not contained in any codimension one foliation.
Cerveau, Dominique, Lins Neto, Alcides
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Generalized transversely projective structure on a transversely holomorphic foliation
International Journal of Mathematics and Mathematical Sciences, 2002 The results of Biswas (2000) are extended to the situation of transversely projective foliations. In particular, it is shown that a transversely holomorphic foliation defined using everywhere locally nondegenerate maps to a projective space ℂℙn, and ...
Indranil Biswas
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