On the existence of geodesic vector fields on closed surfaces

2024/05/15 by Vladimir S. Matveev, Matveev, Vladimir S.
Mathematics · Physics and Astronomy · #37J30 #37J35 #53B20 #53C22 #70H06 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2405.09604

openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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