Displaying similar documents to “Foliations with complex leaves”

Finite determinacy of dicritical singularities in ( ℂ 2 , 0 )

Gabriel Calsamiglia-Mendlewicz (2007)

Annales de l’institut Fourier

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For germs of singularities of holomorphic foliations in ( ℂ 2 , 0 ) which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

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Let ℱ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of ℱ is isomorphic to Z , then ℱ is without holonomy. We also show that if π 2 ( M ) ≅ 0 and the fundamental group of each leaf of ℱ is isomorphic to Z k ( k ∈ Z ≥ 0 ), then ℱ is without holonomy.

On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki (1993)

Annales Polonici Mathematici

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Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.