RC-positivity and rigidity of harmonic maps into Riemannian manifolds Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday

In this paper, we show that every harmonic map from a compact K?hler manifold with uniformly RC-positive curvature to a Riemannian manifold with non-positive complex sectional curvature is constant. In particular, there is no non-constant harmonic map from a compact K¨ahler manifold with positive holomorphic sectional curvature to a Riemannian manifold with non-positive complex sectional curvature.