On the existence of geodesic vector fields on closed surfaces

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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Publication Details

Journal
Theoretical and Applied Mechanics
Published
2025-01-01
DOI
https://doi.org/10.2298/tam241210003m
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
article
Field-Weighted Citation Impact
0.00

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article

On the existence of geodesic vector fields on closed surfaces

Vladimir S. Matveev
Theoretical and Applied Mechanics
Advanced Differential Equations and Dynamical Systems
article

On the existence of geodesic vector fields on closed surfaces

Vladimir S. Matveev
article en

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.

Theoretical and Applied MechanicsVol. 52(1)
Friedrich Schiller University Jena (DE)
Deutsche Forschungsgemeinschaft
Openalex Percentile: Top 88%
Advanced Differential Equations and Dynamical Systems
DOIOpen Access PDFOpenAlex
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On the existence of geodesic vector fields on closed surfaces — Vladimir S. Matveev · Theoretical and Applied Mechanics (2025) | TGRS Research Map | TGRS