Curvature characterization of certain bounded domains of holomorphy

Fangyang Zheng

Vol. 163 (1994), No. 1, 183–188

DOI: 10.2140/pjm.1994.163.183

Abstract

In this note, we study the relation between the existence of a negatively curved complete hermitian metric on a complex manifold M and the product structure of (or contained in) M. We introduce the concept of geometric ranks and give a curvature characterization of the rank one manifolds, which generalizes the previous results of P. Yang and N. Mok (see below). In the proof, we used the old techniques of Yau’s Schwartz lemma and Cheng-Yau’s result on the existence of Kähler-Einstein metrics.

Mathematical Subject Classification 2000

Primary: 32D05

Secondary: 32C17, 32L07, 53C55

Milestones

Received: 18 March 1992

Published: 1 March 1994