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Decomposition of spaces with geodesics contained in compact flats
Author(s):
Bernardo
Molina;
Carlos
Olmos
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3701-3709.
MSC (1991):
Primary 53C35;
Secondary 53C20
Posted:
April 25, 2001
MathSciNet review:
1860505
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Abstract:
We prove a decomposition result for analytic spaces all of whose geodesics are contained in compact flats. Namely, we prove that a Riemannian manifold is such a space if and only if it admits a (finite) cover which splits as the product of a flat torus with simply connected factors which are either symmetric (of the compact type) or spaces of closed geodesics.
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Additional Information:
Bernardo
Molina
Affiliation:
Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
Email:
molina@math.uni-augsburg.de
Carlos
Olmos
Affiliation:
Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
Email:
olmos@mate.uncor.edu
DOI:
10.1090/S0002-9939-01-06008-7
PII:
S 0002-9939(01)06008-7
Keywords:
Compact flats,
rank rigidity,
holonomy
Received by editor(s):
December 16, 1999
Received by editor(s) in revised form:
April 17, 2000
Posted:
April 25, 2001
Additional Notes:
Supported by Universidad Nacional de Córdoba, CONICET and DAAD, partially supported by CONICOR, Secyt-UNC and CIEM
Communicated by:
Christopher Croke
Copyright of article:
Copyright
2001,
American Mathematical Society
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