Asian Journal of Mathematics

Volume 12 (2008)

Number 1

Complex Product Manifolds Cannot be Negatively Curved

Pages: 145 – 150

DOI: https://dx.doi.org/10.4310/AJM.2008.v12.n1.a10

Authors

Harish Seshadri

Fangyang Zheng

Abstract

We show that if M = X × Y is the product of two complex manifolds (of positive dimensions), then M does not admit any complete Kähler metric with bisectional curvature bounded between two negative constants. More generally, a locally-trivial holomorphic fibre-bundle does not admit such a metric.

Keywords

Kähler manifolds, product manifolds, bisectional curvature, negative curvature

2010 Mathematics Subject Classification

Primary 53B25. Secondary 53C40.

Published 1 January 2008