Biharmonic holomorphic maps into Kähler manifolds

We study biharmonic holomorphic maps from an almost Hermitian manifold into a Kähler manifold. First, by a simple observation of the curvature term in the biharmonic equation, we establish non-existence results of biharmonic holomorphic maps into Kähler manifolds with non-positive holomorphic bisectional curvature, which extend the similar results of biharmonic maps between Riemannian manifolds. Second, by applying the second variation formula of biharmonic maps, we prove a non-existence result of stable biharmonic holomorphic maps into complex projective space.