Complex Product Manifolds Cannot be Negatively Curved
Harish Seshadri, Fangyang Zheng · Asian Journal of Mathematics · 2008
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.