ALMOST QUARTER-PINCHED KAHLER METRICS AND CHERN NUMBERS

作者：Deraux Martin^*; Seshadri Harish

来源：Proceedings of the American Mathematical Society, 2011, 139(7): 2571-2576.

DOI：10.1090/S0002-9939-2010-10676-7

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.

• 出版日期2011-7