Displaying similar documents to “About the attractive points of the root functions on the Riemannian foliation.”

De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal, James J. Hebda (1983)

Annales de l'institut Fourier

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We prove that if M is a complete simply connected Riemannian manifold and F is a totally geodesic foliation of M with integrable normal bundle, then M is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

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.

Foliations of surfaces I : an ideal boundary

John N. Mather (1982)

Annales de l'institut Fourier

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Let F be a foliation of the punctured plane P . Any non-compact leaf of F has two ends, which we call leaf-ends. The set ℰ of leaf-ends which converge to the origin has a natural cyclic order. In the case ℰ is infinite, we show that the cyclicly ordered set β , obtained by identifying neighbors in ℰ and filling in the holes according to the Dedeking process, is equivalent to a circle. We show that the set P ∐ β has a natural topology, and it is homeomorphic to S 1 × [ 0 , ∞ ) with respect to this topology. ...