Displaying similar documents to “Foliated G-structures and riemannian foliations.”

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.

Leaves of foliations with a transverse geometric structure of finite type.

Robert A. Wolak (1989)

Publicacions Matemàtiques

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In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.

Nontaut foliations and isoperimetric constants

Konrad Blachowski (2002)

Annales Polonici Mathematici

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We study nontaut codimension one foliations on closed Riemannian manifolds. We find an estimate of some constant derived from the mean curvature function of the leaves of a foliation by some isoperimetric constant of the manifold. Moreover, for foliated 2-tori and the 3-dimensional unit sphere, we find the infimum of the former constants for all nontaut codimension one foliations.

On G-foliations

Robert Wolak (1985)

Annales Polonici Mathematici

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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 the first secondary invariant of Molino's central sheaf

Jesús A. Álvarez López (1996)

Annales Polonici Mathematici

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For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.

Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

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Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.