Kähler manifolds with an almost 1/4-pinched metric

2023/07/28 by Minemyer, Barry · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2307.15550

Abstract

In this paper we construct an almost negatively 1/4-pinched Riemannian metric on a class of compact manifolds recently discovered by Stover and Toledo in [17]. It is known that these manifolds are Kähler and not locally symmetric. These are the first known examples of not locally symmetric Kähler manifolds admitting such a metric and, via the result of Hernandez [9] and Yau and Zheng [18], these manifolds cannot admit a negatively quarter-pinched Riemannian metric. This metric is also interesting because it is a generalization to the complex hyperbolic setting of the famous pinched metric constructed by Gromov and Thurston in [8].

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