Twistor theory for Riemannian symmetric spaces. With applications to harmonic maps of Riemann surfaces (Q1188665)

The book is devoted to the twistor theory for an arbitrary Riemannian manifold \(N^{2n}\) and its application to the theory of harmonic maps. A map \(\phi: M^ 2\to N^{2n}\) is conformal and harmonic if and only if it has a \(J_ 2\)-holomorphic lift to the canonical twistor space \(J(N^{2n})\). In case \(N^{2n}=G/H\) is a Riemannian symmetric space, its twistor space is a flag manifold. The authors study the geometry and topology of flag manifolds. In particular, they construct, for a given harmonic map \(\phi: M^ 2\to G/H\), its \(J_ 2\)-holomorphic lift into the twistor space. Using this approach they obtain a classification of stable harmonic 2-spheres in a Riemannian symmetric space and a Bäcklund transform for harmonic 2-spheres in Lie groups.