Minimal and pluriharmonic immersions between Riemannian manifolds: non-existence and rigidity results

This paper deals with isometric minimal (resp. pluriharmonic) immersions from a Riemannian manifold endowed with a non trivial parallel 2-form into a Riemannian or a Kahlerian manifold of negative (resp, positive) isotropic curvature. Results we obtain generalize some well known non existence and rigidity results concerning minimal and pluriharmonic immersions from Kahlerian manifolds into real or complex space forms. We also obtain some vanishing results for the second Betti number and the space of parallel 2-forms