# On a characterization of the complex hyperbolic space - Mathematics > Differential Geometry

Abstract: Consider a compact K\-{a}hler manifold $M^m$ with Ricci curvature lower bound$Ric M\geq -2m+1 .$ Assume that its universal cover $% \widetilde{M}$ hasmaximal bottom of spectrum $\lambda 1\widetilde{M}% =m^2.$ Then we prove that$\widetilde{M}$ is isometric to the complex hyperbolic space $\Bbb{CH}^m.$

Author: Ovidiu Munteanu

Source: https://arxiv.org/