The constant curvature property of the Wu invariant metric

C.K. Cheung and Kang-Tae Kim

Vol. 211 (2003), No. 1, 61–68

DOI: 10.2140/pjm.2003.211.61

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 Kähler and has constant negative holomorphic curvature in a neighborhood of the spherical boundary points for a large class of domains in ℂⁿ.

Milestones

Received: 9 March 2000

Published: 1 September 2003