Geometriae Dedicata

, Volume 67, Issue 2, pp 129–148 | Cite as

Minimal Geodesics and Nilpotent Fundamental Groups

  • Bernd Ammann


Hedlund [18] constructed Riemannian metrics on n-tori, n ≥ 3 for which minimal geodesics are very rare. In this paper we construct similar examples for every nilpotent fundamental group. These examples show that Bangert's existence results of minimal geodesics [4] are optimal for nilpotent fundamental groups.

minimal geodesics stable norm first Betti number nilpotent Lie groups cocompact discrete subgroups nilmanifolds Hedlund metrics. 


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© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Bernd Ammann
    • 1
  1. 1.Mathematisches Institut der Universität FreiburgFreiburgGermany

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