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On Non-hyperbolic Quasi-convex Spaces
Author(s):
Rafael
Oswaldo
Ruggiero
Journal:
Trans. Amer. Math. Soc.
350
(1998),
665-687.
MSC (1991):
Primary 53C23;
Secondary 53C20, 53C22, 53C40
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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  .
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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