Tohoku Mathematical Journal

Distributions on Riemannian manifolds, which are harmonic maps

Boo-Yong Choi and Jin-Whan Yim

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We find new examples of harmaonic maps between compact Riemannian manifolds. A section of a Riemannian fibration is called harmonic if it is harmonic as a map from the base manifold into the total space. When the fibres are totally geodesic, the Euler-Lagrange equation for such sections is formulated. In the case of distributions, which are sections of a Grassmannian bundle, this formula is described in terms of the geometry of base manifolds. Examples of harmonic distributions are constructed when the base manifolds are homogeneous spaces and the integral submanifolds are totally geodesic. In particular, we show all the generalized Hopf-fibrations define harmonic maps into the Grassmannian bundles with the standard metric.

Article information

Tohoku Math. J. (2), Volume 55, Number 2 (2003), 175-188.

First available in Project Euclid: 11 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Harmonic map distribution homogeneous space


Choi, Boo-Yong; Yim, Jin-Whan. Distributions on Riemannian manifolds, which are harmonic maps. Tohoku Math. J. (2) 55 (2003), no. 2, 175--188. doi:10.2748/tmj/1113246937.

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