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A harmonic map between Riemannian Manifolds can be viewed as a generalization of a Geodesic when the domain Dimension is one, or of a Harmonic Function when the range is a Euclidean Space.
See also Bochner Identity, Euclidean Space, Geodesic, Harmonic Function, Riemannian Manifold
References
Burstal, F.; Lemaire, L.; and Rawnsley, J. ``Harmonic Maps Bibliography.''
http://www.bath.ac.uk/~masfeb/harmonic.html.
Eels, J. and Lemaire, L. ``A Report on Harmonic Maps.'' Bull. London Math. Soc. 10, 1-68, 1978.
Eels, J. and Lemaire, L. ``Another Report on Harmonic Maps.'' Bull. London Math. Soc. 20, 385-524, 1988.