On compact Riemannian manifolds, a metallic structure J with J² = pJ + qI is harmonic exactly when its exterior derivative dJ vanishes, provided p² + 4q ≠ 0.
Fetcu, Harmonic maps between complex Sasakian manifolds , Rend
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Harmonic metallic structures
On compact Riemannian manifolds, a metallic structure J with J² = pJ + qI is harmonic exactly when its exterior derivative dJ vanishes, provided p² + 4q ≠ 0.