Isometric pluriharmonic immersions of Kähler manifolds into semi-Euclidean spaces

Abstract

In this thesis, we prove a classification of isometric pluriharmonic immersions of a Kahler manifold into a semi-Euclidean space, which establishes a generalization of Calabi-Lawson’s theory concerning minimal surfaces in Euclidean spaces. Then we study these immersions for complete Kahler manifolds with low codimensions, and prove, in particular, a cylinder theorem and a Bernstein property. Moreover, we construct new examples of isometric pluriharmonic immersions.