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Decomposition of spaces with geodesics contained in compact flats


Authors: Bernardo Molina and Carlos Olmos
Journal: Proc. Amer. Math. Soc. 129 (2001), 3701-3709
MSC (1991): Primary 53C35; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-01-06008-7
Published electronically: 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: https://doi.org/10.1090/S0002-9939-01-06008-7
Keywords: Compact flats, rank rigidity, holonomy
Received by editor(s): December 16, 1999
Received by editor(s) in revised form: April 17, 2000
Published electronically: 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
Article copyright: © Copyright 2001 American Mathematical Society

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