Negatively curved Kähler metrics on total spaces of a class of vector bundles

Abstract

In this paper we show an abundance of complete Kähler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved Kähler metrics. We prove dimension estimates on holomorphic functions on these manifolds, as well as Liouville theorems for holomorphic mappings between them.

34 pages. Comments are welcome. In this version, we add a remark (Remark 1.13) regarding similar results on the total space of vector bundles. Other parts of the paper remain unchanged