Harmonic maps from ${\mathbb{C}}^n$ to Kahler manifolds

Abstract

In this paper, we shall prove that a harmonic map from ${\mathbb{C}}^n$ ($n\ge 2$) to any Kahler manifold must be holomorphic under an assumption of energy density. It can be considered as a complex analogue of the Liouville type theorem for harmonic maps obtained by Sealey.