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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.27 n.2 Antofagasta ago. 2008

http://dx.doi.org/10.4067/S0716-09172008000200001 

Proyecciones Journal of Mathematics
Vol. 27, Nº 2, pp. 113-144, August 2008.
Universidad Católica del Norte
Antofagasta - Chile


0N CHARACTERIZATION OF RIEMANNIAN MANIFOLDS


IVÁN TRIBUZY 1
VÍCTOR AYALA 1 2
MARCOS M. DINIZ 3
JOSÉ M. M. VELOSO 3

1 Universidade Federal do Amazonas, Brasil
2 Universidad Católica del Norte, Chile
3 Universidade Federal do Pará, Brasil

Correspondencia a:



Abstract
This survey, present some results about characterization of Riemannian manifolds by using notions of convexity. The first part deals with immersed manifolds and the second part gives a characterization for the Euclidean space and for the Euclidean sphere.


Key words : geodesics, convexity, axiomatic geometry, isosceles triangles.

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IVÁN TRIBUZY
Departamento de Matemática
Universidade Federal do Amazonas
Japiim, Manaus - Amazonas, 69077-000
BRASIL
e-mail : argo@ufam.br

VÍCTOR AYALA
Departamento de Matemáticas
Universidad Católica del Norte,
Antofagasta
CHILE
e-mail : vayala@ucn.cl

Departamento de Matemática
Universidade Federal do Amazonas
Japiim, Manaus - Amazonas, 69077-000
BRASIL

MARCOS M. DINIZ
Departamento de Matemática
Universidade Federal do Pará
CCEN
Rua Augusto Correa, 01, CEP 66075-110
Belém - Pará
BRASIL.
e-mail : mdiniz@ufpa.br

JOSÉ M. M. VELOSO
Departamento de Matemática
Universidade Federal do Pará
CCEN
Rua Augusto Correa, 01, CEP 66075-110
Belém - Pará
BRASIL.
e-mail : veloso@ufpa.br

Received : January 2008. Accepted : March 2008