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Killing’s equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion

References:

[1] J. F. Pommaret: **Systems of Partial Differential and Lie Pseudogroups**. Gordon and Breach, New York, 1978. MR 0517402

[2] G. Thompson: **Polynomial constants of motion in a flat space**. J. Math. Phys. 25 (1984), 3474-3478. DOI 10.1063/1.526114 | MR 0767554 | Zbl 0549.70008

[3] G. Thompson: **Killing tensors in spaces of constant curvature**. J. Math. Phys. 27(1986), 2693-2699. DOI 10.1063/1.527288 | MR 0861329 | Zbl 0607.53025

[4] L. P. Eisenhart: **Riemannian Geometry**. Princeton University Press, 1925. MR 1487892

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[7] J. Levine: **Invariant characterizations of two dimensional affine and metric spaces**. Duke Math. J. 15 (1948), 69-77. MR 0025236 | Zbl 0029.41801

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