Surfaces in $$\mathbb {R}^7$$ obtained from harmonic maps in $$S^6$$ .
Tóm tắt
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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