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Cusp closing in rank one symmetric spaces. (English) Zbl 0860.53025
The ends of complete non-compact Riemannian manifolds with pinched negative curvature and finite volume have a very specific structure. In this paper it is shown that they can be closed, keeping the curvature nonpositive, if the universal cover is complex hyperbolic space, and that this is impossible if the universal cover is quaternionic space or the Cayley hyperbolic plane.
Reviewer: W.Ballmann (Bonn)

MSC:
53C20 Global Riemannian geometry, including pinching
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