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.
Dai, Y. J., Shoji, M., & Urakawa, H. (1997). Harmonic maps into Lie groups and homogeneous spaces. Differential Geometry and Its Application, 7(2), 143–160. https://doi.org/10.1016/S0926-2245(96)00045-9