Exponentially harmonic maps between Kähler manifolds

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