I'm curious, does a geodesic of infinite length without self-intersections exist in a Riemannian manifold (M, g) which has finite diameter? There shouldn't be one rigth?
2026-02-22 16:03:48.1771776228
geodesic of infinite length without self-intersections
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Take a line in $\mathbb{R}^2$ with irrational slope, then its image in the flat two torus $\mathbb{R}^2/\mathbb{Z}^2$ is a geodesic that never intersects itself and has infinite length.