S1-invariant harmonic maps from S3 to S2
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Submission date: 15. Mar. 2000
published in: The bulletin of the London Mathematical Society, 32 (2000) 6, p. 729-735
Keywords and phrases: harmonic map, hopf invariant
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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.