Biharmonic maps into compact Lie groups and integrable systems

Abstract

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 compact Lie group (G,h) with the bi-invariant Riemannian metric h is obtained. Using this, all biharmonic curves into compact Lie groups are determined exactly, and all the biharmonic maps of an open domain of ℝ² equipped with a Riemannian metric conformal to the standard Euclidean metric into (G,h) are determined.