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.   In this paper we study harmonic maps from a compact riemannian manifold equiped with a non trivial parallel 2-form, to a Kähler manifold of strongly negative curvature tensor or a riemannian manifold of strictly negative complex sectional curvature. In a first part we set up some rigidity results of Siu type. Then we obtain an upper bound for the rank of such maps in terms of the rank of the 2-form and deduce some vanishing theorems.

Applications harmoniques, applications pluriharmoniques et existence de 2-formes parall�les non nulles