On a characterization of the complex hyperbolic space

Details On a characterization of the complex hyperbolic space On a characterization of the complex hyperbolic space

2008-02-03

arxiv.org/abs/0802.0307v1

Mathematics

Differential Geometry

Scientific paper

Consider a compact K\"{a}hler 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 $\lambda_1(\widetilde{M}%) =m^2.$ Then we prove that
$\widetilde{M}$ is isometric to the complex hyperbolic space $\Bbb{CH}^m.$

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