Abstract
The theory of harmonic maps has been developed since the 1960's (see [2]). In recent years, some authors discussed the harmonicity of “homogeneous” maps between Riemannian homogeneous spaces using the theory of Lie groups. LetG andG′ be compact Lie groups,H andH′ their closed subgroups respectively. Assume that a homomorphism θ:G→G′ mapsH intoH′; then there exists an induced mapf θ:G/H→G′/H′. M.A. Guest gave a necessary and sufficient condition for such a map to be harmonic, whenG/H andG′/H′ are generalized flag manifolds,H=T is a maximal torus andG′ is a unitary group; and he gave some interesting examples (see [3]). We generalize his results to the case of general generalized flag manifoldsG/H, i.e.H is a centralizer of a torus, and give some new examples of harmonic maps.
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