Biharmonic maps into compact Lie groups, and symmetric spaces

Abstract

In this paper, the reduction 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. Due to this formula, all biharmonic curves into compact Lie groups are determined, 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. Biharmonic maps into symmetric spaces are also treated.