Totally geodesic foliations.
В.Ю. Ровенский (1982)
Sibirskij matematiceskij zurnal
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В.Ю. Ровенский (1982)
Sibirskij matematiceskij zurnal
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D. FERUS (1970)
Mathematische Annalen
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Robert A. Wolak (1995)
Annales Polonici Mathematici
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We study the properties of the graph of a totally geodesic foliation. We limit our considerations to basic properties of the graph, and from them we derive several interesting corollaries on the structure of leaves.
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...
Izu Vaisman (1988)
Monatshefte für Mathematik
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Nina Zhukova, Anna Dolgonosova (2013)
Open Mathematics
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The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian...
A. El Kacimi-Alaoui, V. Sergiescu (1984/85)
Mathematische Zeitschrift
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Patrick Coulton (1984)
Mathematische Annalen
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Chaouch, Mohamed A. (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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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...
Elmar Vogt (1982)
Manuscripta mathematica
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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.
Richard Sacksteder (1964)
Annales de l'institut Fourier
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