Isothermic surfaces obtained from harmonic maps in S6
Keyword(s):
The harmonicity of a smooth map from a Riemann surface into the 6-dimensional sphere S6 amounts to the closeness of a certain 1-form that can be written in terms of the nearly K?hler structure of S6. We will prove that the immersions F in R7 obtained from superconformal harmonic maps in S3 ? S6 by integration of the corresponding closed 1-forms are isothermic. The isothermic surfaces so obtained include a certain class of constant mean curvature surfaces in R3 that can be deformed isometrically through isothermic surfaces into non-spherical pseudo-umbilical surfaces in R7.
2002 ◽
Vol 40
(01)
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pp. 121-124
2007 ◽
Vol 129
(4)
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pp. 1145-1181
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2013 ◽
Vol 220
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pp. 316-323
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2010 ◽
Vol 362
(06)
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pp. 2845-2857
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2012 ◽
Vol 61
(1)
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pp. 123-131
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