Abstract
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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Stepanov, S.E., Shandra, I.G. Seven Classes of Harmonic Diffeomorphisms. Mathematical Notes 74, 708–716 (2003). https://doi.org/10.1023/B:MATN.0000009004.63465.da
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DOI: https://doi.org/10.1023/B:MATN.0000009004.63465.da