Advertisement

Potential Analysis

, Volume 2, Issue 3, pp 295–298 | Cite as

A note on the classification of holomorphic harmonic morphisms

  • Sigmundur Gudmundsson
  • Ragnar Sigurdsson
Article

Abstract

In this note we give a complete classification of those holomorphic maps φ:U→ℂ n defined on open and connected subsets of ℂ m which are harmonic morphisms.

Mathematics Subject Classifications (1991)

58E20 58G32 32A10 

Key words

Harmonic morphisms Brownian motions holomorphic maps 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baird, P.:Harmonic Maps with Symmetry, Harmonic Morphisms and Deformation of Metrics, Research Notes in Mathematics87, Pitman (1983).Google Scholar
  2. 2.
    Baird, P.: Harmonic morphisms and circle actions on 3- and 4-manifolds,Ann. Inst. Fourier, Grenoble 40 (1990), 177–212.Google Scholar
  3. 3.
    Baird, P.: Riemannian twistors and Hermitian structures on low-dimensional space forms,J. Math. Phys. 33 (1992), 3340–3350.Google Scholar
  4. 4.
    Baird, P. and Eells, J.: A conservation law for harmonic maps, inGeometry Symposium Utrecht 1980, Lecture Notes in Mathematics894, Springer (1981), pp. 1–25.Google Scholar
  5. 5.
    Baird, P. and Wood, J. C.: Harmonic morphisms and conformal foliation by geodesics of three-dimensional space forms,J. Australian Math. Soc. (A)51 (1991), 118–153.Google Scholar
  6. 6.
    Darling, R. W. R.: Martingales in manifolds — definition, examples and behaviour under maps, inSéminaire de Probabilités XVI 1980/81. Supplément: Géométrie Differentielle Stochastique, Lecture Notes in Mathematics921, Springer (1982), 217–236.Google Scholar
  7. 7.
    Gudmundsson, S.: Harmonic morphisms between spaces of constant curvature,Proc. Edinburgh Math. Soc. 36 (1992), 133–143.Google Scholar
  8. 8.
    Gudmundsson, S. and Wood, J. C.: Multivalued harmonic morphisms,Math. Scand. 72 (1994), (to appear).Google Scholar
  9. 9.
    Fuglede, B.: Harmonic morphisms between Riemannian manifolds,Ann. Inst. Fourier 28 (1978), 107–144.Google Scholar
  10. 10.
    Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions,J. Math. Kyoto Univ. 19 (1979), 215–229.Google Scholar
  11. 11.
    Wood, J. C.: Harmonic morphisms and Hermitian structures on Einstein 4-manifolds,Intern. J. Math. 3 (1992), 415–439.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Sigmundur Gudmundsson
    • 1
  • Ragnar Sigurdsson
    • 1
  1. 1.Science InstituteUniversity of IcelandReykjavikIceland

Personalised recommendations