Integrable geodesic flows with simultaneously diagonalisable quadratic integrals

2024/03/21 by Agafonov, Sergey I., Matveev, Vladimir S.
#37J35 #70H06 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2403.14319

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.

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