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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of harmonic foliations by variations of the metric


Authors: Michael D. Hvidsten and Philippe Tondeur
Journal: Proc. Amer. Math. Soc. 98 (1986), 359-362
MSC: Primary 57R30; Secondary 53C12, 58D17, 58E11, 58E20
MathSciNet review: 854047
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Abstract: In this paper it is shown that a harmonic Riemannian foliation of a Riemannian manifold can be characterized as being a critical point of the energy of the foliation under certain variations of the manifold's Riemannian metric. These variations are those induced by the flows of vector fields on the manifold.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854047-4
PII: S 0002-9939(1986)0854047-4
Article copyright: © Copyright 1986 American Mathematical Society