Foliations admitting transverse systems of differential equations
Robert Wolak (1988)
Compositio Mathematica
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Robert Wolak (1988)
Compositio Mathematica
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Robert A. Wolak (1989)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
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.
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.
Escobales, Richard H.jun. (2003)
International Journal of Mathematics and Mathematical Sciences
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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.
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.