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

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