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

Abstract

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

References in corpus (2)

• Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models
• Surfaces in ${\mathbb{R}}^{N^2-1}$ based on harmonic maps $S^2\to C{P}^{N-1}$