Integrable geodesic flows with simultaneously diagonalisable quadratic integrals

Arnold Mathematical Journal 2026 Open access

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Authors: Sergey I. Agafonov, Vladimir Sergeevich Matveev
DOI: 10.56994/armj.011.004.001
Cited by: 0

Abstract

We show that if 𝑛 functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an 𝑛-dimensional manifold are simultaneously diagonalisable at the tangent space to every point, then they come from the Stäckel construction, so the metric admits orthogonal separation of variables.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Mathematical Dynamics and Fractals Advanced Differential Equations and Dynamical Systems

Publication details

Journal / source
Arnold Mathematical Journal
Publisher
Association for Mathematical Research
Volume
011
Issue
004
Pages
1–1
Publication date
14 February 2026
Language
EN