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Isothermic Surfaces Obtained From Harmonic Maps in S 6

Rui Pacheco

Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Covilhã, Portugal

Abstract: The harmonicity of a smooth map from a Riemann surface into the 6-dimensional sphere S 6 amounts to the closeness of a certain 1-form that can be written in terms of the nearly Kähler structure of S 6 . We will prove that the immersions F in 7 obtained from superconformal harmonic maps in S 3 S 6 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 3 that can be deformed isometrically through isothermic surfaces into non-spherical pseudo-umbilical surfaces in 7 .

Keywords: Harmonic maps, isothermic surfaces, parallel mean curvature, pseudo-umbilical surfaces, seven dimensional cross product

Classification (MSC2000): 53C43,53C42, 53A10,53A07

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Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.

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