Geodesic
On the existence of geodesic vector fields on closed surfaces
Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 109

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We construct an example of a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
DOI : 10.2298/TAM241210003M
Classification : 37J30, 53C22, 37J35, 70H06, 53B20
Keywords: geodesic vector fields, Riemann normal coordinates, geodesic normal coordinates, semi-geodesic coordinates, integrable geodesic flow 
Vladimir S. Matveev. On the existence of geodesic vector fields on closed surfaces. Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 109 . doi: 10.2298/TAM241210003M
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