Examples of constant mean curvature surfaces obtained from harmonic maps to the two sphere

1997 ◽  
Vol 226 (1) ◽  
pp. 127-146 ◽  
Author(s):  
Manuel Ritoré
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Harmonic Maps ◽  
Constant Mean Curvature Surfaces

scholarly journals Isothermic surfaces obtained from harmonic maps in S6

2018 ◽  
Vol 103 (117) ◽  
pp. 175-180
Author(s):  
Rui Pacheco
Keyword(s):  
Riemann Surface ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Harmonic Maps ◽  
Dimensional Sphere ◽  
Constant Mean Curvature Surfaces ◽  
Isothermic Surfaces ◽  
Smooth Map

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.

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