On the fundamental groups of negatively curved manifolds with finite volume

Goto, Midori S.

doi:10.1090/S0002-9939-1979-0529223-7

On the fundamental groups of negatively curved manifolds with finite volume
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by Midori S. Goto PDF

Proc. Amer. Math. Soc. 75 (1979), 99-103 Request permission

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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