Abstract
A nondegenerate, Riemannian metric is called integrable if its geodesic flow is integrable. An integrable nondegenerate Riemannian metric is called linear-quadratic if its geodesic flow admits an additional integral which is linear or quadratic in the momenta.
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References
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Fomenko, A.T. (1993). Linear-Quadratic Metrics “Approximate” any Nondegenerate, Integrable Riemannian Metric on the 2-Sphere and the 2-Torus. In: Babelon, O., Kosmann-Schwarzbach, Y., Cartier, P. (eds) Integrable Systems. Progress in Mathematics, vol 115. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0315-5_11
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DOI: https://doi.org/10.1007/978-1-4612-0315-5_11
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