English

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.

Keywords

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

R2 v1 2026-06-28T16:28:39.212Z