Almost quarter-pinched Kähler metrics and Chern numbers

Details Almost quarter-pinched Kähler metrics and Chern numbers Almost quarter-pinched Kähler metrics and Chern numbers

2009-12-18

arxiv.org/abs/0912.3726v1

Proceedings of the American Mathematical Society 139 (2011) 2571-2576

Mathematics

Differential Geometry

Scientific paper

10.1090/S0002-9939-2010-10676-7

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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