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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the fundamental groups of negatively curved manifolds with finite volume


Author: Midori S. Goto
Journal: Proc. Amer. Math. Soc. 75 (1979), 99-103
MSC: Primary 53C20; Secondary 22E40
MathSciNet review: 529223
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Abstract: We will prove that if M is a complete, simply connected riemannian manifold with sectional curvature K, $ a \leqslant K < 0$, for $ a > 0$ and $ \Gamma $ a properly discontinuous group of isometries of M acting freely on M with volume $ (M/\Gamma )$ finite, then $ M/\Gamma $ is compact if and only if $ \Gamma $ consists of hyperbolic elements.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0529223-7
PII: S 0002-9939(1979)0529223-7
Keywords: Fundamental group, negatively curved manifold, hyperbolic isometry, Dirichlet region
Article copyright: © Copyright 1979 American Mathematical Society