Applications harmoniques, applications pluriharmoniques et existence de 2-formes parallèles non nulles

Abstract.

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.