Explicit construction of harmonic two-spheres in \(SU(3)/SO(3)\) (Q2772934)

Analyzing the Cartan embedding of \(SU(3)/SO(3)\) into \(SU(3)\) and applying \textit{J. C. Wood}'s construction of harmonic maps from \(S^2\) to \(SU(3)\) [Proc. Lond. Math. Soc. 58, 608-624 (1989; Zbl 0679.58015)], the author finds those harmonic maps \(S^2\to SU(3)\) that, factoring through the Cartan embedding, descend to harmonic maps \(S^2\to SU(3)/SO(3)\). In this way the author obtains a description of all harmonic maps from the sphere \(S^2\) into \(SU(3)/SO(3)\), a non-inner compact symmetric space of dimension \(5\) and rank \(2\).