Complex hyperbolic Gromov-Thurston metrics and almost $\frac{1}{4}$-pinched K\"{a}hler manifolds

Author:

Barry Minemyer

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Metric Geometry (math.MG)

journal:

date:

2023-07-27 16:00:00

Abstract

In this paper we construct an almost negatively $\frac{1}{4}$-pinched Riemannian metric on a class of compact manifolds that, via previous work, was already known to be K\"{a}hler and not locally symmetric. This is the first known example of such manifolds and, via the result of Hernandez [7] and Yau and Zheng [14], these manifolds cannot admit a negatively quarter-pinched Riemannian metric. This metric is also interesting because it is the complex hyperbolic analogue to the famous pinched metric constructed by Gromov and Thurston in [6].

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