CLASSIFICATION OF PLURIHARMONIC MAPS FROM COMPACT COMPLEX MANIFOLDS WITH POSITIVE FIRST CHERN CLASS INTO COMPLEX GRASSMANN MANIFOLDS

Dedicated to Professor Masaru Takeuchi on his sixtieth birthday

Abstract

We prove that any pluriharmonic map from a compact complex manifold with positive first Chern class (defined outside a certain singularity set of codimension at least two) into a complex Grassmann manifold of rank two is explicitly constructed from a rational map into a complex projective space. Under some restrictions on dimension and rank of the domain manifold and the target manifold, respectively, we also prove that similar results hold for other complex Grassmann manifolds as targets.