Minimal Geodesics and Nilpotent Fundamental Groups
by
Bernd Ammann


Minimal Geodesics and Nilpotent Fundamental Groups (.dvi , .dvi.gz , .ps oder .ps.gz)
Geom. Dedic. 67 no. 2, 129-148, 1997
DOI: 10.1023/A:1004963800510

Abstract

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.

Mathematics Subject Classification

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