Yang-Mills theory and uniformization
Consider a stable holomorphic vector bundle over a compact, Hermitian manifold. For various hypothesis concerning the dimension of the manifold and whether or not it is Kähler it has been shown by Narasimhan and Seshadri, Donaldson, Uhlenbeck and Yau and Buchdahl that the bundle admits a Hermitian-Yang-Mills connection. In this paper the author introduces the concept of a stable system of Hodge bundles and proves that over a Kähler manifold it admits a Hermitian-Yang-Mills connection. If certain chern classes vanish this leads to a complex variation of the Hodge structure and thereby a criterion for the manifold to be uniformized by a bounded symmetric domain.
uniformized by a bounded symmetric domain
scientific article; zbMATH DE number 4034117