Minimal Geodesics and Nilpotent Fundamental Groups

Mathematics – Differential Geometry

Scientific paper

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23 pages, uses pstricks.sty

Scientific paper

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.

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