Pluriharmonic maps into Kähler symmetric spaces and Sym’s formula

Abstract

A construction due to Sym and Bobenko recovers constant mean curvature surfaces in euclidean 3-space from their harmonic Gauss maps. We generalize this construction to higher dimensions and codimensions replacing the surface by a complex manifold and the sphere (the target space of the Gauss map) by a Kahler symmetric space of compact type with its standard embedding into the Lie algebra $${\mathfrak{g}}$$ of its transvection group. Thus we obtain a new class of immersed Kahler submanifolds of $${\mathfrak{g}}$$ and we derive their properties.