Minimal Geodesics and Nilpotent Fundamental Groups
by
Bernd Ammann
Minimal Geodesics and Nilpotent Fundamental Groups
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Geom. Dedic. 67 no. 2,
129-148, 1997
DOI: 10.1023/A:1004963800510
Hedlund constructed Riemannian metrics on $n$-tori, $n \geq 3$
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
are optimal for nilpotent fundamental
groups.
Primary 53C22, Secondary 22E25, 20F18
Keywords
minimal geodesics, stable norm,
first Betti number, nilpotent Lie groups, cocompact discrete subgroups,
nilmanifolds, Hedlund metrics
Bernd Ammann, 4.1.1999