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arXiv · 0912.3726

Almost quarter-pinched K\"ahler metrics and Chern numbers

Martin Deraux·Harish Seshadri
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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.

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Martin Deraux, Harish Seshadri. 2009-12-18. Almost quarter-pinched K\"ahler metrics and Chern numbers. https://doi.org/10.1090/s0002-9939-2010-10676-7

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