Exponentially harmonic maps between Kähler manifolds

Abstract

In this paper, we show Liouville-type theorems for exponentially harmonic maps and p-harmonic maps between Kähler manifolds. We then study the quadratic form of an exponentially harmonic map of Kähler manifolds and its applications. We also prove that if [Formula: see text] is an exponentially harmonic map from a compact Kähler manifold [Formula: see text] into a Kähler manifold [Formula: see text] with constant energy density such that the curvature of [Formula: see text] is strongly semi-negative, then [Formula: see text] is holomorphic or antiholomorphic.