On the existence of geodesic vector fields on closed surfaces

Vladimir S. Matveev

Institut für Mathematik, Friedrich Schiller Universität Jena, Jena, Germany

Abstract: We construct an example of a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.

Keywords: geodesic vector fields, Riemann normal coordinates, geodesic normal coordinates, semi-geodesic coordinates, integrable geodesic flow.

MSC: 37J30, 53C22, 37J35, 70H06, 53B20

Received: 10.12.2024

Language: English

DOI: 10.2298/TAM241210003M