Ukrainian Mathematical Journal

, Volume 55, Issue 4, pp 588–600 | Cite as

Harmonic Properties of Gauss Mappings in H3

  • L. A. Masal'tsev


We consider some harmonic mappings related to hyperbolic Gauss mappings and Gauss mappings in the Obata sense.


Harmonic Mapping Gauss Mapping Harmonic Property Hyperbolic Gauss Mapping 
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  1. 1.
    E. A. Ruh and J. Vilms, “The tension field of Gauss map,” Trans. Amer. Math. Soc., 199, 569-573 (1970).Google Scholar
  2. 2.
    C. L. Epstein, “The hyperbolic Gauss map and quasiconformal reflection,” J. Reine Angew. Math., 372, 96-135 (1986).Google Scholar
  3. 3.
    R. Bryant, “Surfaces of mean curvature 1 in hyperbolic space,” Asterisque, 154/155, 321-347 (1987).Google Scholar
  4. 4.
    M. Obata, “The Gauss map of immersion of Riemannian manifolds in spaces of constant curvature,” J. Different. Geom., 2, No. 2, 217-223 (1968).Google Scholar
  5. 5.
    A. A. Borisenko and Yu. A. Nikolaevskii, “Grassmann manifolds and Grassmann image of submanifolds,” Usp. Mat. Nauk, 46, Issue 2, 41-83 (1991).Google Scholar
  6. 6.
    A. A. Borisenko, “On surfaces of nonpositive extrinsic curvature in spaces of constant curvature,” Mat. Sb., 114, No. 3, 339-354 (1981).Google Scholar
  7. 7.
    M. Kokubu, “Weierstrass representation for minimal surfaces in hyperbolic space,” Tohoku Math. J., 49, 367-377 (1997).Google Scholar
  8. 8.
    H. Urakawa, Calculus of Variations and Harmonic Maps, American Mathematical Society, Providence (1993).Google Scholar
  9. 9.
    H. Rosenberg, Bryant Surfaces, Preprint No. 99-4, University Paris-VII, Paris (1999).Google Scholar
  10. 10.
    . H. C. Wente, “Constant mean curvature immersions of Enneper type,” Mem. Amer. Math. Soc., 478, 1-78 (1992).Google Scholar
  11. 11.
    . J. A. Wolf, Spaces of Constant Curvature, University of California-Berkeley, Berkeley (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • L. A. Masal'tsev
    • 1
  1. 1.Kharkov UniversityKharkov

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