Seshadri, Harish; Zheng, Fangyang Complex product manifolds cannot be negatively curved. (English) Zbl 1147.53317 Asian J. Math. 12, No. 1, 145-149 (2008). Summary: We show that if \(M = X \times Y\) 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. Cited in 1 ReviewCited in 6 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:product manifolds; bisectional curvature; negative curvature × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid