Complex product manifolds cannot be negatively curved

Harish Seshadri; Fangyang Zheng

Complex product manifolds cannot be negatively curved

Differential Geometry 2008-01-03 v1 Complex Variables

Authors: Harish Seshadri , Fangyang Zheng

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 K\"ahler 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 holomorphic vector bundles kähler metrics

Cite

@article{arxiv.0801.0284,
  title  = {Complex product manifolds cannot be negatively curved},
  author = {Harish Seshadri and Fangyang Zheng},
  journal= {arXiv preprint arXiv:0801.0284},
  year   = {2008}
}

Comments

6 Pages. To appear in The Asian Journal of Mathematics

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