Exponentially harmonic maps between Kähler manifolds

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.