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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A global correspondence between
CMC-surfaces in $S^3$ and pairs
of non-conformal harmonic maps into $S^2$


Authors: R. Aiyama, K. Akutagawa, R. Miyaoka and M. Umehara
Journal: Proc. Amer. Math. Soc. 128 (2000), 939-941
MSC (2000): Primary 53C42; Secondary 53A10
Published electronically: October 25, 1999
MathSciNet review: 1707134
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

R. Aiyama
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan
Email: aiyama@sakura.cc.tsukuba.ac.jp

K. Akutagawa
Affiliation: Department of Mathematics, Shizuoka University, Shizuoka 422-8529, Japan
Email: smkacta@ipc.shizuoka.ac.jp

R. Miyaoka
Affiliation: Department of Mathematics, Sophia University, Tokyo 102-8554, Japan
Email: r-miyaok@hoffman.cc.sophia.ac.jp

M. Umehara
Affiliation: Department of Mathematics, Hiroshima University, Hiroshima 739-8526, Japan
Email: umehara@math.sci.hiroshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05580-X
PII: S 0002-9939(99)05580-X
Received by editor(s): April 15, 1998
Published electronically: October 25, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society