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MiS Preprint
24/2000

S^1-invariant harmonic maps from S^3 to S^2

Guofang Wang

Abstract

In this note, we show that a homotopy class of [S³, S²] admits an S¹-invariant harmonic map if and only if its Hopf invariant is ±k² for some integer k, where S³ is the unit 3-sphere and S² is a 2-sphere with an arbitrary metric.

Received:
Mar 15, 2000
Published:
Mar 15, 2000
MSC Codes:
58E20
Keywords:
harmonic map, hopf invariant

Related publications

inJournal
2000 Repository Open Access
Guofang Wang

S1-invariant harmonic maps from S3 to S2

In: The bulletin of the London Mathematical Society, 32 (2000) 6, pp. 729-735