This article is cited in 5 papers

Seven Classes of Harmonic Diffeomorphisms

S. E. Stepanov^a, I. G. Shandra<sup>b

a</sup> Vladimir State Pedagogical University
^b Finance Academy under the Government of the Russian Federation

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.

UDC: 514.764.25

Received: 20.12.2001
Revised: 05.06.2003

DOI: 10.4213/mzm308

 English version: Mathematical Notes, 2003, 74:5, 708–716

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