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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Displaying similar documents to “Riemannian foliations with parallel or harmonic basic forms”
A characterization of harmonic foliations by the volumepreserving property of the normal geodesic flow.
On the harmonic and Killing tensor field on a compact Riemannian manifold.
Tsagas, Gr., Bitis, Gr. (2001)
Balkan Journal of Geometry and its Applications (BJGA)
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Deforming metrics of foliations
Vladimir Rovenski, Robert Wolak (2013)
Open Mathematics
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Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the...
Harmonic conformal flows on manifolds of constant curvature
Amine Fawaz (2007)
Open Mathematics
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We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.
Differential forms, Weitzenböck formulae and foliations.
Hansklaus Rummler (1989)
Publicacions Matemàtiques
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The Weitzenböck formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor. In the first part, we shall describe a certain "differential algebra formalism" which seems to be a more natural frame for those formulae than the usual calculations in local coordinates. In this formalism there appear some interesting differential operators...
Harmonic morphisms and subharmonic functions.
Choi, Gundon, Yun, Gabjin (2005)
International Journal of Mathematics and Mathematical Sciences
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Foliated G-structures and riemannian foliations.
Robert A. Wolak (1990)
Manuscripta mathematica
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The diffeomorphism group of a Riemannian foliation.
Macias Virgós, E. (1997)
General Mathematics
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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.
Transversal biwave maps
Yuan-Jen Chiang, Robert A. Wolak (2010)
Archivum Mathematicum
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In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map. We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either. We prove that if is a transversal biwave map satisfying certain condition, then is a transversal wave map. We finally study the transversal conservation laws of transversal biwave maps.