Immersed surfaces in Lie algebras associated to primitive harmonic maps (Q357863)

The construction to recover a constant mean curvature surface in \(\mathbb{R}^3\) from the one-parameter family of harmonic maps associated to its Gauss map \(F:M\rightarrow S^2\) (where \(M\) is a simply connected Riemann surface) given in [\textit{A. Sym}, ``Soliton surfaces and their applications (Soliton geometry from spectral problems)'', Lect. Notes Phys. 239, 154--231 (1986; \url{doi:10.1007/3-540-16039-6_6}) and \textit{A. I. Bobenko}, Russ. Math. Surv. 46, No. 4, 1--45 (1991); translation from Usp. Mat. Nauk 46, No. 4(280), 3--42 (1991; Zbl 0755.53004)] was generalized in [\textit{J.-H. Eschenburg} and \textit{P. Quast}, Math. Z. 264, No. 2, 469--481, erratum 483--484 (2010; Zbl 1189.31009)] by replacing \(S^2\) with a Kähler symmetric space \(N\) of compact type. The present paper gives a further generalization, by replacing the target \(N\) with a general flag manifold \(G/K\) and by considering immersions of \(M\) in the Lie algebra of \(G\) associated to primitive harmonic maps.