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The systolic constant of orientable Bieberbach 3-manifolds

Chady El MirJacques Lafontaine — 2013

Annales de la faculté des sciences de Toulouse Mathématiques

A compact manifold is called if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. We study the optimal systolic ratio of compact 3 -dimensional orientable Bieberbach manifolds which are not tori, and prove that it cannot be realized by a flat metric. We also highlight a metric that we construct on one type of such manifolds ( C 2 ) which has interesting...

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