CLASSIFICATION OF PLURIHARMONIC MAPS FROM COMPACT COMPLEX-MANIFOLDS WITH POSITIVE 1ST CHERN CLASS INTO COMPLEX GRASSMANN MANIFOLDS

We prove that any pluriharmonic map from a compact complex manifold wi th positive first Chern class (defined outside a certain singularity s et of codimension at least two) into a complex Grassmann manifold of r ank two is explicitly constructed from a rational map into a complex p rojective space. Under some restrictions on dimension and rank of the domain manifold and the target manifold, respectively, we also prove t hat similar results hold for other complex Grassmann manifold as targe ts.