Displaying similar documents to “Foliations with Degenerate Gauss maps on ℙ 4 ”

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.

The diffeomorphism group of a Lie foliation

Gilbert Hector, Enrique Macías-Virgós, Antonio Sotelo-Armesto (2011)

Annales de l’institut Fourier

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We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus T n , n ≥ 2 . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are ± Id and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for T 2 , P. Iglesias...

Flows of flowable Reeb homeomorphisms

Shigenori Matsumoto (2012)

Annales de l’institut Fourier

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We consider a fixed point free homeomorphism h of the closed band B = ℝ × [ 0 , 1 ] which leaves each leaf of a Reeb foliation on B invariant. Assuming h is the time one of various topological flows, we compare the restriction of the flows on the boundary.

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.