Harmonic maps into Lie groups and homogeneous spaces

Abstract

The tension field of a smooth map of an arbitrary Riemannian manifold into any homogeneous space (G/K, h) with an invariant Riemannian metric h is calculated. As its applications, a characterization of harmonic maps into any homogeneous space is given and all harmonic maps of the standard Euclidean space (ℝm, go) into a Lie group (G, h) with left invariant Riemannian metric h, of the form f(x1, . . . , xm) = exp(x1X1) . . . exp(xmXm) are determined.