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arXiv · 0804.1419

Sur la géométrie systolique des variétés de Bieberbach

Chady Elmir·Jacques Lafontaine
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Abstract

The systole of a compact non simply connected Riemannian manifold is the smallest length of a non-contractible closed curve ; the systolic ratio is the quotient $(\mathrm{systole})^n/\mathrm{volume}$. Its supremum on the set of all the riemannian metrics, is known to be finite for a large class of manifolds, including the $K(π,1)$. We study the optimal systolic ratio of compact, 3-dimensional non orientable Bieberbach manifolds, and prove that it cannot be realized by a flat metric.

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Chady Elmir, Jacques Lafontaine. 2008-06-03. Sur la géométrie systolique des variétés de Bieberbach. https://arxiv.org/abs/0804.1419

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