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

Article copyright:
© Copyright 1986
American Mathematical Society