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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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|
|Additional Information:||Copyright of this article belongs to American Mathematical Society.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||30 Aug 2011 06:54|
|Last Modified:||30 Aug 2011 06:54|
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