多复变数Einstein空间中的Schwarz引理

<正> 本文主要的目的是来证明定理1.设■域是 n 个复变数■=(z~1,…,z~n)空间中的简单域且为Einstein空间(不失一般性,不妨假设其 Ricci 曲率为-1),其Bergman度量为

ON THE SCHWARZ LEMMA IN EINSTEIN SPACES OF SEVERAL COMPLEX VARIABLES

The main theorem of the present note isTheorem 1.Let D be a simple domain of n complex variables(z)=(z~1,…,z~n)with Bergman metric(?)where(?)Let D be an Einstein space with constant Ricci curvature-1.Let w~((j))= f~((j))(z~1,…,z~n),j= 1,2,…,n be a pseudo-conformal mappingwhich maps D onto a domain D′in w-space.If we can define a Hermi-tian metric(?) in D′ such that the Ricci curvature of D′ defined by this metric is notgreater than -1 and h