RC-positivity and rigidity of harmonic maps into Riemannian manifolds

Abstract

In this paper, we show that every harmonic map from a compact Kähler 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 Kähler manifold with positive holomorphic sectional curvature to a Riemannian manifold with non-positive complex sectional curvature.