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On deformations of holomorphic foliations

Joan Girbau, Marcel Nicolau (1989)

Annales de l'institut Fourier

Given a non-singular holomorphic foliation on a compact manifold M we analyze the relationship between the versal spaces K and K tr of deformations of as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of parametrized by an analytic space K f isomorphic to π - 1 ( 0 ) × Σ where Σ is smooth and π : K K tr is the forgetful map. The map π is shown to be an epimorphism in two situations: (i) if H 2 ( M , Θ f ) = 0 , where Θ f is the sheaf of...

On the automorphism group of strongly pseudoconvex domains in almost complex manifolds

Jisoo Byun, Hervé Gaussier, Kang-Hyurk Lee (2009)

Annales de l’institut Fourier

In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...

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