On the holomorphicity of harmonic maps from compact Kähler manifolds to hyperbolic Riemann surfaces

Abstract

We give a sufficient condition in order that a harmonic map from a compact Kähler manifold with negative first Chern class to a compact hyperbolic Riemann surface be ± \pm holomorphic. The above condition generalizes that of Eells and Wood concerning harmonic maps between Riemann surfaces. As a corollary we get a generalization of Kneser’s theorem.