Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-15T01:25:29.158Z Has data issue: false hasContentIssue false
  • English
  • Français

On harmonic maps between S3 and S2 of prescribed Hopf invariant

Published online by Cambridge University Press:  24 October 2008

Andrea Ratto
Andrea Ratto
Affiliation:
Mathematical Institute, University of Warwick, and I.C.T.P. Trieste, Italy
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we prove the following

Theorem. Each element of the group π3(S2) = ℤ can be rendered harmonic, i.e. admits a harmonic representative, provided that the domain S3is given a suitable riemannian metric.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 273 - 276
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baird, P.. Harmonic maps with symmetry, harmonic morphisms and deformations of metrics. Research Notes in Mathematics no. 87 (Pitman, 1983).Google Scholar
[2]Eells, J. and Lemaire, L.. A report on harmonic maps. Bull. London Math. Soc. 10 (1978), 1–68.Google Scholar
[3]Eells, J. and Polking, J. C.. Removable singularities of harmonic maps. Indiana Univ. Math. J. 33 (1984), 859–871.CrossRefGoogle Scholar
[4]Smith, R. T.. Harmonic mappings of spheres. Ph.D. thesis, Warwick University (1972).CrossRefGoogle Scholar
[5]Smith, R. T.. Harmonic mappings of spheres. Amer. J. Math. 97 (1975), 364–385.Google Scholar