In this paper, the formulation of 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 is obtained. Using this, all the biharmonic curves into symmetric spaces are determined, and all the biharmonic maps of an open domain of ℝ2 with the standard Riemannian metric into (G/K,h) are characterized exactly.
"Biharmonic maps into symmetric spaces and integrable systems." Hokkaido Math. J. 43 (1) 105 - 136, February 2014. https://doi.org/10.14492/hokmj/1392906096