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Geometriae Dedicata

, Volume 194, Issue 1, pp 65–80 | Cite as

Surfaces in \(\mathbb {R}^7\) obtained from harmonic maps in \(S^6\).

  • Pedro Morais
  • Rui PachecoEmail author
Original Paper
  • 138 Downloads

Abstract

We will investigate the local geometry of the surfaces in the 7-dimensional Euclidean space associated to harmonic maps from a Riemann surface \(\varSigma \) into \(S^6\). By applying methods based on the use of harmonic sequences, we will characterize the conformal harmonic immersions \(\varphi :\varSigma \rightarrow S^6\) whose associated immersions \(F:\varSigma \rightarrow \mathbb {R}^7\) belong to certain remarkable classes of surfaces, namely: minimal surfaces in hyperspheres; surfaces with parallel mean curvature vector field; pseudo-umbilical surfaces; isotropic surfaces.

Keywords

Harmonic maps Minimal surfaces Parallel mean curvature Pseudo-umbilical surfaces Seven dimensional cross product 

Mathematics Subject Classification (2010)

53C43 53C42 53A10 53A07 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Centro Matemática e Aplicações (CMA-UBI)Universidade da Beira InteriorCovilhãPortugal

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