On the existence of geodesic vector fields on closed surfaces
Differential Geometry
2026-04-07 v2
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.
Cite
@article{arxiv.2405.09604,
title = {On the existence of geodesic vector fields on closed surfaces},
author = {Vladimir S. Matveev},
journal= {arXiv preprint arXiv:2405.09604},
year = {2026}
}
Comments
4 pages, 1 figure. Certain misprints corrected