论文标题
Kähler歧管的谐波图
Harmonic maps from Kähler manifolds
论文作者
论文摘要
该报告试图清晰地介绍谐波图理论，从复杂的和Kähler歧管到Riemannian歧管。在回顾了由Eells-Sampson和Bochner Technique发起的Riemannian流形之间的谐波理论之后，我们专门研究Kähler域并引入Pluriharmonic Maps。由于SIU和Sampson及其主要后果，我们证明了精致的Bochner公式，例如SIU的刚性结果。我们还将应用程序介绍到非绘制类型的对称空间及其与Mostow刚性的关系。最后，我们解释了该理论对非亚伯杂货的对应关系的关键作用，该对应关系与紧凑型Kähler歧管和希格斯束的模量空间有关。
This report attempts a clean presentation of the theory of harmonic maps from complex and Kähler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps between Riemannian manifolds initiated by Eells--Sampson and the Bochner technique, we specialize to Kähler domains and introduce pluriharmonic maps. We prove a refined Bochner formula due to Siu and Sampson and its main consequences, such as the strong rigidity results of Siu. We also recount the applications to symmetric spaces of noncompact type and their relation to Mostow rigidity. Finally, we explain the key role of this theory for the nonabelian Hodge correspondence relating the character variety of a compact Kähler manifold and the moduli space of Higgs bundles.
