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Decomposition of spaces with geodesics contained in compact flats |
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| Authors: | Bernardo Molina Carlos Olmos |
| Institution: | Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina ; Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina |
| 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. |
| Keywords: | Compact flats rank rigidity holonomy |
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