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  • Research Article
  • Open Access

The anosov theorem for infranilmanifolds with an odd-order abelian holonomy group

Fixed Point Theory and Applications20062006:63939

  • Received: 9 September 2004
  • Accepted: 21 July 2005
  • Published:


We prove that for any continuous map of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the techniques developed for solvmanifolds.


  • Differential Geometry
  • Computational Biology
  • Holonomy Group
  • Abelian Holonomy


Authors’ Affiliations

Department of Mathematics, Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, Etienne Sabbelaan 53, Kortrijk, 8500, Belgium


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© K. Dekimpe et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.