A global correspondence between CMC-surfaces in 𝑆³ and pairs of non-conformal harmonic maps into 𝑆²

Aiyama, R.; Akutagawa, K.; Miyaoka, R.; Umehara, M.

doi:10.1090/S0002-9939-99-05580-X

A global correspondence between CMC-surfaces in $S^3$ and pairs of non-conformal harmonic maps into $S^2$
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by R. Aiyama, K. Akutagawa, R. Miyaoka and M. Umehara PDF

Proc. Amer. Math. Soc. 128 (2000), 939-941 Request permission

Abstract:

We show there is a global correspondence between branched constant mean curvature (i.e. CMC-) immersions in $S^3/\{\pm 1\}$ and pairs of non-conformal harmonic maps into $S^2$ in the same associated family. Furthermore, we give two applications.

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