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 (R m , g 0) into a Lie group ( G, h) with left invariant Riemannian metric h, of the form ƒ ( x 1, …, x m ) = exp( x 1 X 1) … exp( x mX m ) are determined.
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