Fuchsian manifolds

Chen, Su Shing

doi:10.1090/S0002-9947-1975-0362135-1

Fuchsian manifolds
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Trans. Amer. Math. Soc. 203 (1975), 247-256 Request permission

Abstract:

Recently Eberlein and O’Neill have investigated Riemannian manifolds of negative sectional curvature. For visibility manifolds, they have obtained a classification into three types: parabolic, axial and fuchsian. Fundamental groups of fuchsian manifolds of finite type will be investigated. The main theorem is that isometry groups of certain (not necessarily compact) fuchsian manifolds are finite. Fundamental groups of fuchsian manifolds of finite type are not amenable. The spectral radius of the random matrix of the fundamental group of a compact Riemannian manifold of negative sectional curvature is less than one.

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