Almost quarter-pinched Kähler metrics and Chern numbers
arXiv:0912.3726 · doi:10.1090/S0002-9939-2010-10676-7
Abstract
We prove that compact Kähler manifolds whose sectional curvatures are close to 1/4-pinched have ratios of Chern numbers close to the corresponding ratios of a complex hyperbolic space form. We deduce that the Mostow-Siu surfaces (and their three-dimensional analogues constructed by the first author) do not admit Kähler metrics with pinching close to 1/4.