Surfaces in $$\mathbb {R}^7$$ obtained from harmonic maps in $$S^6$$S6. |
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Authors: | Pedro Morais Rui Pacheco |
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Institution: | 1.Centro Matemática e Aplica??es (CMA-UBI),Universidade da Beira Interior,Covilh?,Portugal |
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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. |
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