Almost quarter-pinched K\"ahler metrics and Chern numbers
Differential Geometry
2011-04-14 v1
Abstract
We prove that compact K\"ahler 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 K\"ahler metrics with pinching close to 1/4.
Keywords
Cite
@article{arxiv.0912.3726,
title = {Almost quarter-pinched K\"ahler metrics and Chern numbers},
author = {Martin Deraux and Harish Seshadri},
journal= {arXiv preprint arXiv:0912.3726},
year = {2011}
}