# Killing's equations in dimension two and systems of finite type

Mathematica Bohemica (1999)

- Volume: 124, Issue: 4, page 401-420
- ISSN: 0862-7959

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topThompson, Gerard. "Killing's equations in dimension two and systems of finite type." Mathematica Bohemica 124.4 (1999): 401-420. <http://eudml.org/doc/248448>.

@article{Thompson1999,

abstract = {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.},

author = {Thompson, Gerard},

journal = {Mathematica Bohemica},

keywords = {Killing’s equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion; Killing's equations; symmetric linear connections; linear integrals of motion; system of finite type; quadratic integrals of motion},

language = {eng},

number = {4},

pages = {401-420},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Killing's equations in dimension two and systems of finite type},

url = {http://eudml.org/doc/248448},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Thompson, Gerard

TI - Killing's equations in dimension two and systems of finite type

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 4

SP - 401

EP - 420

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/248448

ER -

## References

top- J. F. Pommaret, Systems of Partial Differential and Lie Pseudogroups, Gordon and Breach, New York, 1978. (1978) MR0517402
- G. Thompson, 10.1063/1.526114, J. Math. Phys. 25 (1984), 3474-3478. (1984) Zbl0549.70008MR0767554DOI10.1063/1.526114
- G. Thompson, 10.1063/1.527288, J. Math. Phys. 27(1986), 2693-2699. (1986) Zbl0607.53025MR0861329DOI10.1063/1.527288
- L. P. Eisenhart, Riemannian Geometry, Princeton University Press, 1925. (1925) MR1487892
- L. P. Eisenhart, Non-Riemannian Geometry, Amer. Math. Soc. Colloquium Publications 8, New York, 1927. (1927) MR1466961
- I. Anderson G. Thompson, The Inverse Problem of the Calculus of Variations for Ordinary differential Equations, Memoirs Amer. Math. Soc. 473, 1992. (1992) MR1115829
- J. Levine, Invariant characterizations of two dimensional affine and metric spaces, Duke Math. J. 15 (1948), 69-77. (1948) Zbl0029.41801MR0025236
- E. G. Kalnins W. Miller, 10.1137/0511089, SIAM J. Math. Anal. 11 (1980), 1011-1026. (1980) MR0595827DOI10.1137/0511089

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