A characterization of harmonic foliations by the volumepreserving property of the normal geodesic flow.
Kim, Hobum (2002)
International Journal of Mathematics and Mathematical Sciences
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Kim, Hobum (2002)
International Journal of Mathematics and Mathematical Sciences
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Al-Aqeel, Adnan, Bejancu, Aurel (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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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.
Macias Virgós, E. (1997)
General Mathematics
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Paul A. Schweitzer (2011)
Annales de l’institut Fourier
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Every open manifold of dimension greater than one has complete Riemannian metrics with bounded geometry such that is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry....
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.
Mohamed Tahar Kadaoui Abbassi, Giovanni Calvaruso, Domenico Perrone (2009)
Annales mathématiques Blaise Pascal
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We produce new examples of harmonic maps, having as source manifold a space of constant curvature and as target manifold its tangent bundle , equipped with a suitable Riemannian -natural metric. In particular, we determine a family of Riemannian -natural metrics on , with respect to which all conformal gradient vector fields define harmonic maps from into .