F-Harmonic Maps in Kahler Geometry

Abstract

Let u be an F-harmonic map between Kahler manifolds of finite dimensions. When is u holomorphic or anti-holomorphic? In the special case of a harmonic map, Y. T. Siu gave an affirmative answer when the target manifold is a Riemannian manifold of semi-strongly negative curvature. In other cases, such as p-harmonic and exponentially harmonic maps, answers to the above question were less satisfactory. For the general case of F-harmonic maps, this thesis investigates the holomorphicity of F-harmonic maps from a complex space form to a Kahler manifold and obtains Liouville-type theorems.