从复流形到对称空间的多重调和映射

Pluriharmonic Maps from Complex Manifolds Into Symmetric Spaces

本文首先证明了从复流形到对称空间的多重调和映射空间与扩张提升空间之间在相差一规范变换下存在一一对应,并给出确定的环路群在扩张提升空间的作用,因而也给出多重调和映射空间上的作用.其次,利用环路群及其代数的Iwasawa分解给出从Cn到对称空间的有限型的多重调和映射不同于文[1]中的刻划.

In this paper, we prove that there exists a one to one correspondence between the space of pluriharmonic maps from complex manifold into symmetric spaces and the space of extended lifts up to a gauge transformation. And we determine the action of certain loop group on the space of extended lifts. So we give the action of space of pluriharmonic maps from complex manifold into symmetric spaces. We also give a description of finite type pluiharmonic maps from Cn into symmetric spaces by using the Iwasawa decompositions of loop groups and their loop algebras, which is different from that of [1].