Displaying similar documents to “On the theorem of Frobenius for complex vector fields”

On vector fields in C without a separatrix.

J. Olivares-Vázquez (1992)

Revista Matemática de la Universidad Complutense de Madrid

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A family of germs at 0 of holomorphic vector fields in C without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

On algebraic sets invariant by one-dimensional foliations on 𝐂 P ( 3 )

Marcio G. Soares (1993)

Annales de l'institut Fourier

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We consider the problem of extending the result of J.-P. Jouanolou on the density of singular holomorphic foliations on C P ( 2 ) without algebraic solutions to the case of foliations by curves on C P ( 3 ) . We give an example of a foliation on C P ( 3 ) with no invariant algebraic set (curve or surface) and prove that a dense set of foliations admits no invariant algebraic set.

Unfoldings of holomorphic foliations.

Xavier Gómez-Mont (1989)

Publicacions Matemàtiques

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The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.

On the smoothness of Levi-foliations.

D. E. Barrett, John Erik Fornaess (1988)

Publicacions Matemàtiques

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We study the regularity of the induced foliation of a Levi-flat hypersurface in C, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.

Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

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Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p ∑ i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform...

Foliations of M 3 defined by ℝ 2 -actions

Jose Luis Arraut, Marcos Craizer (1995)

Annales de l'institut Fourier

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In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of ℝ 2 .