Asian Journal of Mathematics
Volume 12 (2008)
Complex Product Manifolds Cannot be Negatively Curved
Pages: 145 – 150
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.
Kähler manifolds; product manifolds; bisectional curvature; negative curvature
2010 Mathematics Subject Classification
Primary 53B25. Secondary 53C40.