Geodesic
Seven Classes of Harmonic Diffeomorphisms
Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 752-761

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We deduce two necessary and sufficient conditions for a diffeomorphism $f\ :M\to\overline M$ of a Riemannian manifold $(M,g)$ onto a Riemannian manifold $(\overline M,\bar g)$ to be harmonic. Using the representation theory of groups, we define in an intrinsic way seven classes of such harmonic diffeomorphisms and partly describe the geometry of each class. 
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     author = {S. E. Stepanov and I. G. Shandra},
     title = {Seven {Classes} of {Harmonic} {Diffeomorphisms}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a11/}
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S. E. Stepanov; I. G. Shandra. Seven Classes of Harmonic Diffeomorphisms. Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 752-761. http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a11/