Geodesic
The seven classes of harmonic diffeomorphisms and their geometry
Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 139-154
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One of the present authors classified harmonic diffeomorphisms between Riemannian manifolds [1]. This paper is devoted to the study of the local and global geometry of certain classes of harmonic diffeomorphisms. 
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S. E. Stepanov; I. G. Shandra. The seven classes of harmonic diffeomorphisms and their geometry. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 139-154. http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a13/