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Mat. Zametki, 2003, Volume 74, Issue 5, Pages 752–761 (Mi mz308)  

This article is cited in 4 scientific papers (total in 4 papers)

Seven Classes of Harmonic Diffeomorphisms

S. E. Stepanova, I. G. Shandrab

a 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.

DOI: https://doi.org/10.4213/mzm308

Full text: PDF file (236 kB)
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English version:
Mathematical Notes, 2003, 74:5, 708–716

Bibliographic databases:

UDC: 514.764.25
Received: 20.12.2001
Revised: 05.06.2003

Citation: S. E. Stepanov, I. G. Shandra, “Seven Classes of Harmonic Diffeomorphisms”, Mat. Zametki, 74:5 (2003), 752–761; Math. Notes, 74:5 (2003), 708–716

Citation in format AMSBIB
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\transl
\jour Math. Notes
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. V. Zudina, S. E. Stepanov, I. G. Shandra, “Equiaffine mappings”, Russian Math. (Iz. VUZ), 51:8 (2007), 25–32  mathnet  crossref  mathscinet  zmath
    2. Hinterleitner I., Mikes J., “On the Equations of Conformally-Projective Harmonic Mappings”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, eds. Kielanowski P., Odzijewicz A., Schlichenmaier M., Voronov T., Amer Inst Physics, 2007, 141–148  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Hinterleitner I., “Conformally-Projective Harmonic Mappings of Equidistant Manifolds with the Friedmann Models as Example”, Aplimat 2007 - 6th International Conference, Pt II, ed. Kovacova M., Slovak Univ Tech Bratislava, 2007, 97–102  mathscinet  isi
    4. Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566  mathscinet  isi
  • Математические заметки Mathematical Notes
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