Foliated G-structures and riemannian foliations.
Robert A. Wolak (1990)
Manuscripta mathematica
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Robert A. Wolak (1990)
Manuscripta mathematica
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P. Tondeur, Maung Min-Oo, E.A. Ruh (1991)
Journal für die reine und angewandte Mathematik
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Christopher Deninger, Wilhelm Singhof (2001)
Annales de l’institut Fourier
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We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
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 , a simple characterization of this geometrical property is proved.
Macias Virgós, E. (1997)
General Mathematics
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José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does...
Robert A. Blumenthal, James J. Hebda (1983)
Annales de l'institut Fourier
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We prove that if is a complete simply connected Riemannian manifold and is a totally geodesic foliation of with integrable normal bundle, then 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.
Paweł G. Walczak (1992)
Annales Polonici Mathematici
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Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.
Dirk Töben (2014)
Annales de l’institut Fourier
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We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type...
Xosé Masa (1992)
Commentarii mathematici Helvetici
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A. El Kacimi-Alaoui, V. Sergiescu (1984/85)
Mathematische Zeitschrift
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