On a characterization of the complex hyperbolic space

Ovidiu Munteanu

On a characterization of the complex hyperbolic space

Differential Geometry 2008-02-05 v1

Authors: Ovidiu Munteanu

Abstract

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 $\Bbb{CH}^m.$

Keywords

kähler manifolds hyperbolic surfaces riemannian geometry

Cite

@article{arxiv.0802.0307,
  title  = {On a characterization of the complex hyperbolic space},
  author = {Ovidiu Munteanu},
  journal= {arXiv preprint arXiv:0802.0307},
  year   = {2008}
}

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