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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
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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

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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