Geodesic
Killing's equations in dimension two and systems of finite type
Mathematica Bohemica, Tome 124 (1999) no. 4, pp. 401-420

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MR Zbl
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.
DOI : 10.21136/MB.1999.125998
Classification : 34A26, 35A05, 53B05, 53Z05, 70G45, 70H33
Keywords: Killing’s equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion 
Thompson, G. Killing's equations in dimension two and systems of finite type. Mathematica Bohemica, Tome 124 (1999) no. 4, pp. 401-420. doi: 10.21136/MB.1999.125998
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[1] J. F. Pommaret: Systems of Partial Differential and Lie Pseudogroups. Gordon and Breach, New York, 1978. | MR

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

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

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

[5] L. P. Eisenhart: Non-Riemannian Geometry. Amer. Math. Soc. Colloquium Publications 8, New York, 1927. | MR

[6] I. Anderson G. Thompson: The Inverse Problem of the Calculus of Variations for Ordinary differential Equations. Memoirs Amer. Math. Soc. 473, 1992. | MR

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

[8] E. G. Kalnins W. Miller: Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations. SIAM J. Math. Anal. 11 (1980), 1011-1026. | DOI | MR

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