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Some conditions ensuring the vanishing of harmonic differential forms with applications to harmonic maps and Yang-Mills theory

Published online by Cambridge University Press:  24 October 2008

H. C. J. Sealey
H. C. J. Sealey
Affiliation:
University of Utah, Salt Lake City
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Extract

In (5) it is shown that if m ≽ 3 then there is no non-constant harmonic map φ: ℝm → Sn with finite energy. The method of proof makes use of the fact that the energy functional is not invariant under conformal transformations. This fact has also allowed Xin(9), to show that any non-constant-harmonic map φ:Sm → (N, h), m ≽ 3, is not stable in the sense of having non-negative second variation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 441 - 452
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

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