Decomposition of spaces with geodesics contained in compact flats

Molina, Bernardo; Olmos, Carlos

doi:10.1090/S0002-9939-01-06008-7

Decomposition of spaces with geodesics contained in compact flats
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by Bernardo Molina and Carlos Olmos PDF

Proc. Amer. Math. Soc. 129 (2001), 3701-3709 Request permission

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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