Deraux, Martin and Seshadri, Harish
(2011)
*Almost quarter-pinched Kähler metrics and Chern numbers.*
In: Proceedings of the American Mathematical Society, 139
(7).
pp. 2571-2576.

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## Abstract

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to American Mathematical Society. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Id for Latest eprints |

Date Deposited: | 30 Aug 2011 06:54 |

Last Modified: | 30 Aug 2011 06:54 |

URI: | http://eprints.iisc.ac.in/id/eprint/39742 |

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