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Geometriae Dedicata

, Volume 136, Issue 1, pp 95–110 | Cite as

Sur la géométrie systolique des variétés de Bieberbach

  • Chady El Mir
  • Jacques Lafontaine
Original Paper

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 (systole) n /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.

Keywords

Systole Systolic ratio Singular Riemannian metric Bieberbach manifold 

Mathematics Subject Classification (2000)

53C23 53C22 53C20 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institut de Mathématiques et Modélisation de Montpellier CNRS, UMR 5149Université Montpellier 2Montpellier Cedex 5France

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