Publications de l’Institut Mathématique, Nouvelle Série Vol. 103[117] 
Isothermic Surfaces Obtained From Harmonic Maps in ${S}^{6}$Rui PachecoCentro de Matemática e Aplicações (CMAUBI), Universidade da Beira Interior, Covilhã, PortugalAbstract: The harmonicity of a smooth map from a Riemann surface into the 6dimensional sphere ${S}^{6}$ amounts to the closeness of a certain 1form that can be written in terms of the nearly Kähler structure of ${S}^{6}$. We will prove that the immersions $F$ in ${\mathbb{R}}^{7}$ obtained from superconformal harmonic maps in ${S}^{3}\subset {S}^{6}$ by integration of the corresponding closed 1forms are isothermic. The isothermic surfaces so obtained include a certain class of constant mean curvature surfaces in ${\mathbb{R}}^{3}$ that can be deformed isometrically through isothermic surfaces into nonspherical pseudoumbilical surfaces in ${\mathbb{R}}^{7}$. Keywords: Harmonic maps, isothermic surfaces, parallel mean curvature, pseudoumbilical surfaces, seven dimensional cross product Classification (MSC2000): 53C43,53C42, 53A10,53A07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.
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