MSC:
34A26,
35A05,
53B05,
53Z05,
70G45,
70H33 | MR 1722875 | Zbl 0952.70014 | DOI: 10.21136/MB.1999.125998

Full entry |
PDF
(3.0 MB)
Feedback

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

[5] L. P. Eisenhart: **Non-Riemannian Geometry**. Amer. Math. Soc. Colloquium Publications 8, New York, 1927. MR 1466961

[6] I. Anderson G. Thompson: **The Inverse Problem of the Calculus of Variations for Ordinary differential Equations**. Memoirs Amer. Math. Soc. 473, 1992. MR 1115829

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

[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 10.1137/0511089 | MR 0595827