Abstract

Let K\\G be an irreducible Hermitian symmetric space of noncompact type and Γ⊂G a closed torsionfree discrete subgroup. Let X be a compact Kähler manifold and ρ:π1(X,x0)⟶Γ a homomorphism such that the adjoint action of ρ(π1(X,x0)) on the Lie algebra Lie(G) is completely reducible. A theorem of Corlette associates to ρ a harmonic map H:X⟶K\\G/Γ. We give a criterion for this harmonic map H to be holomorphic. We also give a criterion for it to be anti-holomorphic.

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