Biharmonic maps into symmetric spaces and integrable systems (Q2445033)

This paper describes the biharmonic map equation in terms of the Maurer-Cartan form for all smooth maps of a compact Riemannian manifold into a Riemannian symmetric space (\(G/K,h\)) induced from the bi-invariant Riemannian metric \(h\) on \(G\). By this formula, all biharmonic curves into symmetric spaces are determined, and all the biharmonic maps from an open domain of \(\mathbb{R}^2\) equipped with the standard Riemannian metric into (\(G/K,h\)) are determined.