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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Non-hyperbolic Quasi-convex Spaces


Author: Rafael Oswaldo Ruggiero
Journal: Trans. Amer. Math. Soc. 350 (1998), 665-687
MSC (1991): Primary 53C23; Secondary 53C20, 53C22, 53C40
MathSciNet review: 1451615
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Abstract: We show that if the universal covering of a compact Riemannian manifold with no conjugate points is a quasi-convex metric space then the following assertion holds: Either the universal covering of the manifold is a hyperbolic geodesic space or it contains a quasi-isometric immersion of $Z\times Z$.


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Additional Information

Rafael Oswaldo Ruggiero
Affiliation: Pontificia Universidade Católica do Rio de Janeiro, PUC-Rio, Dep. de Matemática, Rua Marqués de São Vicente 225, Gávea, Rio de Janeiro, Brasil

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02075-3
PII: S 0002-9947(98)02075-3
Keywords: Conjugate points, quasi-convex space, Gromov-hyperbolic space, quasi-isometric immersion
Received by editor(s): April 25, 1994
Received by editor(s) in revised form: April 12, 1996
Additional Notes: Partially supported by CNPq of Brazilian Government
The present paper was developed while the author was visiting at the École Normale Supérieure in Lyon from 09/93 to 08/94
Article copyright: © Copyright 1998 American Mathematical Society