The constant curvature property of the Wu invariant metric

Abstract

We investigate the property of the Wu invariant metric on a certain class of psuedoconvex domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys the complex hyperbolic curvature property in such cases. Namely, the Wu invariant metric is Kahler and has constant negative holomorphic curvature in a neighborhood of the spherical boundary points for a large class of domains in C-n.