Hermitian metrics of semi-negative curvature on quotients of bounded symmetric domains
Let (X,g) be a locally symmetric Hermitian manifold of finite volume uniformized by an irreducible bounded symmetric domain of rank\(\geq 2\). Let h be a Hermitian metric on X such that (X,h) carries semi-negative curvature (i.e. its curvature tensor is semi-negative in the sense of Griffiths). Under the assumption that h is dominated by a constant multiple of g, \textit{N. Mok} [Ann. Math., II. Ser. 125, 105-152 (1987; Zbl 0616.53040)] proved that, in fact, \(h=cg\) for some constant \(c>0.\) The purpose of the present article is to prove the above result without any further assumption on the domination of h. The paper also contains a study of volume forms of negative Ricci curvature defined outside some ``partially exceptional'' divisors of a complex manifold.
scientific article; zbMATH DE number 4094313
scientific article