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arXiv · 0802.0307

On a characterization of the complex hyperbolic space

Ovidiu Munteanu
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Abstract

Consider a compact Kähler manifold $M^m$ with Ricci curvature lower bound $Ric_M\geq -2(m+1) .$ Assume that its universal cover $% \widetilde{M}$ has maximal bottom of spectrum $λ_1(\widetilde{M}%) =m^2.$ Then we prove that $\widetilde{M}$ is isometric to the complex hyperbolic space $\Bbb{CH}^m.$

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Ovidiu Munteanu. 2008-02-03. On a characterization of the complex hyperbolic space. https://arxiv.org/abs/0802.0307

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