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Displaying similar documents to “Lie algebras of vector fields and codimension one foliations.”

Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, C 2 -foliated manifolds of codimension one, having all leaves proper, are shown to be C ∞ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class C ∞ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class C r and of class C r + 1 for every nonnegative integer r .

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

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For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is ≤ 2 , a simple characterization of this geometrical property is proved.