n functionally independent commutative quadratic integrals for a geodesic flow that are simultaneously diagonalisable imply the metric comes from the Stäckel construction and admits orthogonal separation of variables.
Orthogonal separation of variables for spaces of constant curvature
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abstract
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and the St\"ackel matrices.
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math.DG 1years
2024 1verdicts
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Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
n functionally independent commutative quadratic integrals for a geodesic flow that are simultaneously diagonalisable imply the metric comes from the Stäckel construction and admits orthogonal separation of variables.