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Complex Product Manifolds Cannot be Negatively Curved

Seshadri, Harish and Zheng, Fangyang (2008) Complex Product Manifolds Cannot be Negatively Curved. In: Asian Journal of Mathematics, 12 (1). pp. 145-149.

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Abstract

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 Kahler metric with bisectional curvature bounded between two negative constants. More generally, a locally-trivial holomorphic fibre-bundle does not admit such a metric.

Item Type: Journal Article http://www.intlpress.com/AJM/AJM-v12.php... Copyright of this article belongs to International Press. Division of Physical & Mathematical Sciences > Mathematics 04 Aug 2008 08 Jan 2013 06:08 http://eprints.iisc.ernet.in/id/eprint/15442