Higher dimensional Möbius bands and their boundaries



We give a characterisation of Bieberbach manifolds which are geodesic boundaries of a compact flat manifold, and discuss the low dimensional cases, up to dimension 4.

Mathematics Subject Classification

53C20 53C22 53C23 


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The authors would like to thank Andrzej Szczepański for giving the description of 4-dimensional Bieberbach manifolds with zero first Betti number by the use of the useful CARAT package. They also thank the anonymous referee for his comments and remarks.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Applications (LaMA-Liban)Université LibanaiseTripoliLebanon
  2. 2.Institut Montpelliérain Alexander Grothendieck (UMR 5149)Université de MontpellierMontpellier Cedex 5France

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