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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fuchsian manifolds


Author: Su Shing Chen
Journal: Trans. Amer. Math. Soc. 203 (1975), 247-256
MSC: Primary 53C20
MathSciNet review: 0362135
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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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DOI: https://doi.org/10.1090/S0002-9947-1975-0362135-1
Keywords: Fuchsian manifold, negative sectional curvature, limit set, properly discontinuous group
Article copyright: © Copyright 1975 American Mathematical Society